Usually, whenever I think of a random character build idea, I can arrive at something that is at least in the ballpark. But this time I am stumped.

The idea is for a melee-oriented, preferably strength-based character who has access to a lot of self-healing/regeneration.

No greater requirement than that. Any race, class, spells (but not magic items), feats, whatever it takes.

The intent would be to play something akin to how I'd imagine a half-troll would play, but I recognize that's probably a taller order than it may seem. Make it function, the style and aesthetics can be secondary.

Thanks!

Regenerative health can be a tall order.

temporary hitpoints can fit the somewhat effectively. Heroism spell is decent at lower levels. The temporary hitpoints regen an amount equal to the casting modifier every turn that is close if you can keep concentration. Human variant/custom lineage using their free feat at level 1 for heavy armor master can make this feel even more effective by further reducing damage each instance.

the fiend warlock regenerating temporary hitpoints equal to its warlock level+charisma can be effective. Between kills, short rest spell slots, and armor of agathys it can feel pretty tanky.

divine soul sorcerer with life cleric dip or perhaps full life cleric can get access to the regenerate spell. Regenerate would be effected by the disciple of life feature and could be a good use of the extend metamagic feature.

A Celestial warlock who chooses path of the chain has access to a pool f D6s that can be utilized with a bonus action to heal. Gift of the ever living ones invocation just maxes out those d6s for healing on yourself so long as your familiar is nearby.

Tomb of levistus gives a large amount of temporary hitpoints as a reaction and recharges on a short rest. It does come at the cost of incapacitation so concentration ends automatically if this has to be used.

high level champion heals quite a bit but that’s high level and probably not applicable.

beast barbarian bite while raging can heal a bit. Battlerager recklessly attacking also regens some temporary hitpoints.

Hmm, MotM Goliaths have a reaction feature for reducing damage that I suppose you could flavor as a healing factor instead, but it's PB/LR, not constant. Dwarves also have a racial feat that allows them to roll a Hit Die and regain the roll plus CON when they take the Dodge action. Class-wise there's precious little that actually has a regen-like effect, that's pretty much a monster-exclusive feature. Best bet is probably one of the Barbarian or Fighter subclasses that incorporate gaining temporary HP. Specifically I'd say either the Tundra variant of the Storm Herald or (if your DM allows it) the Battlerager Barbarian or the Samurai Fighter.

I'd agree that the Goliath damage reduction could be a good start along with the idea that a Goliath also reflects the size of a half-troll as well. While the fire features of the Fiend Warlock don't seem too thematic for a half-troll, the Dark One's Blessing does give temp HP for killing things. The Fathomless patron's 6th level Guardian Coil is another way to reduce damage. The Fiendish Vigor invocation also gives you the ability to cast False Life at will, providing temp HP. Cloak of Flies might also be thematic for a half-troll, but has nothing to do with regeneration. The fighter's second wind feature could be themed as a regeneration-type effect as well.

If your DM would allow the One D&D playtest version of Barkskin, that could work well also. It gives temp HP that regenerate every round for up to an hour (concentration).

Thank you very much for the replies. This is exactly what I was looking for!

I don't think I would make such a character but it is always fun to theorycraft.

If you're at a table that allows Blood Hunter, the Order of the Mutant subclass does have a regeneration-like feature available at 7th level:

Reconstruction

Prerequisite: 7th level

For 1 hour, at the start of each of your turns when you have at least 1 hit point but fewer hit points than half your hit point maximum, you regain hit points equal to your proficiency bonus. However, your speed is reduced by 10 feet during this time.

The main trouble is the specific mechanic you're looking for is flavoured wrong for players. Damphirs and Beast Barbarians get lots of self-healing abilities but they are flavouring as bite attacks not as Regen. Everything else is just temp HP which doesn't stack so there are pretty limited options there. 

Hm.... Ah got it!

Goliath + Mercy Monk who smack themselves in the face to use their Hands of Healing for their regen. Add in 3 levels of Rune Knight and you're golden. (except your MADD as all hell but let's just assume you rolled beautiful stats.)

It's not the best mechanically, but I think that a Goliath Beast Barbarian does the most to feel like a D&D troll. For one, Goliaths are often just called "Half-Giants", and a Troll is a type of giant in the first place. So creating a character that is half-troll, it's easier to explain that they don't quite have the natural regenerative powers of a full-blooded troll, so they need to consume other creatures to fully activate it. This is probably the easiest way to get a Troll-like character that has Troll-like features (Trolls do have a natural bite attack, after all), without needing to do a lot of reflavoring of magic abilities to pull off.

I think the big problem is just that, well... it's not a very mechanically solid subclass. Or at the very least, it's not the best choice much of the time... the Bite form for Beast Barbarian is generally considered the weakest option... the tail does the same amount of damage, but it also has reach and a unique reaction to increase your AC that you can use every round; not just when your health is below half.

I would start by basing it on its stat block.

https://www.dndbeyond.com/monsters/17040-troll

You can ignore the attributes and roll your own. 

Would make an interesting Monk

A paladin that uses Lay On Hands on themself to "regenerate". Maybe Oath of the Ancients?

Wildspacer Background, Circle of Spores Druid (20 levels), for your race, the Hill Dwarf gives you another hit point per level, but you'd probably go with a Bugbear or Ork to be closer to the Troll concept you're going for:  Hit points out the ears, and with endless Wildshapes to activate your spores, you can regenerate those temporary hit points faster than most characters can burn through them, and you have healing spells just in case they do get into your regular hit points.  And you can attack with Strength, Dexterity, or Wisdom as desired depending on what method of attacks you choose to use.

Champion Fighter gets regeneration, but it comes online well after most campaigns have ended.

Is homebrew acceptable? I made a troll race with a regen ability. Basically you can use your action to spend hit dice as if you just short rested. It's nice because it feels like a lot of people don't use/understand hit dice rules, and this provides incentive to do so.

Quote from lexgamer >>

Is homebrew acceptable? I made a troll race with a regen ability. Basically you can use your action to spend hit dice as if you just short rested. It's nice because it feels like a lot of people don't use/understand hit dice rules, and this provides incentive to do so.

 That sounds like a re-flavored Autognome. (If Mending is cast on one of them, it can spend a hit die to roll a hit die and regain the hit points from it).  I like it.

Another option would be:

Hill Dwarf + Dwarven Fortitude + Mercy Monk + Beast Barbarian. I'd go 5 Beast Barb then 4 Mercy Monk then the rest beast Barb. Beast Barb + Monk is a relatively powerful build assuming your DM allows your Beast Barb claws to count as Unarmed Strikes. 

One of the better temp hp per turn options is artilerist artificer. The turret can be hand held so it could be a like a common trope of a troll carrying a favorite doll, item ect. 

The temp hp is great when you get it but it doesn't hold up at higher levels.

With the right build/reflavor artificer mc could work well.