I want to create a CR10 boss that is able to heal himself completely when the players believe they killed him. Possible more than once based on their actions. A minion would bring him a “canister” capable of healing of him. If I run it as his base 209 hp and heal him then his effective HP would be 418 and he wouldn’t be a CR10. If they let him get another canister effective would be 627. What is the best way to this? should I set it to 104 and just heal him up when he hits 0? I figured some of you might have more creative solutions.

Theros has monsters like that. They’re Mythic Monsters, and typically have a much higher CR than you’re looking at, but it could be a place to start. 

I am a huge fan of boss fights being in stages. I will generally create two/three separate creatures that represent the same BBEG and tweak their powers based on the stage of the fight. The initial one might be holding back due to arrogance, and the final one might be desperately flailing.

If you do a scene transition between versions it gives you a chance to narrate some cinematic action and the fight becomes less like one huge CR creature and more like 2-3 back-to-back encounters. Maybe the ogre smashes through a wall and retreats to its cave, maybe the wizard teleports into the next room, whatever. It gives the party a moment to breathe but should only be 1-2 rounds. It also lets the BBEG shake off any persistent status effects to start fresh in round 2 and it forces/allows the party to reposition themselves. You can also hit them with a lair action or something during the transition if the battle has been less challenging than you wanted.

For your guy, I'd probably try to do something a bit more bulletprooof than a minion running in. There's a chance the party could have some kind of ability or spell that could stop it before it heals the boss. I'd probably have the canister on the guy and have him use it as a last resort, or if you want to do a scene transition maybe he charges into the next room and dives into a vat of the stuff or something.

The easy way to balance a boss with multiple health bars is to just treat it as multiple encounters in a row (also, if you've got a Freeza or whatever with multiple stages, this has the advantage of working even when the boss has different abilities at different stages). However, what you're describing is more of a puzzle monster: he's not actually beatable until someone figures out the trick. Depending on how obvious the trick is, I'd probably figure he resets at least once but probably not several times unless the trick is really obscure.

This is great! I’ll test some of this out! I will reconsider the minion and run it as a multi-stage encounter!

I was recently running my players through Hoard of the Dragon Queen, and there's a particular enemy in the module who has a feature that, when reduced to zero HP, he comes back with 20 hp for one last burst of attack. I liked that idea, but I wanted to expand on it... so what I came up with was that certain high-profile members of the cult of Tiamat, after being killed, would re-animate as an Undead at half their health, but now they suddenly have a breath weapon attack. It helped to reinforce the danger they were facing and had a thematically interesting effect as part of it.