I gave one of my characters a book that, once read, granted him the ability to cast the Acid Splash cantrip once per short rest.  Is there a way to create this item/feat/whatever in the Homebrew item builder that would show up as an attack with a charge on his DNDBeyond character sheet?

From a little bit of tinkering it seems yes and no....yes you can create a book/wondrous item to give the cantrip once per short rest and it will show up on his character sheet but I cannot find a way to remove the "at will" tag next to the acid splash listing in the character sheet.

Create a feat.  Add a custom action to it which duplicates the effects of Acid Splash, or just add an action called 'Acid Splash' as well as the spell Acid Splash.  The custom action can be set to a short-rest recharge; set this recharge, then save the action.  Edit the action a second time (yes, this is necessary, the submenu you need doesn't show up until the short-rest recharge is saved), and find the "Limited Uses" submenu below the regular fields for Custom Action.  Set use count to 1, save the Limited Use entry.

You will now see 'Acid Splash' as an action on the character sheet, with a single charge.  If you added the spell as well, that shows up as a regular cantrip in the spell list and you'll have to rely on your player not being a jerk.  if you duplicated the spell, you'll need to either configure it for cantrip scaling on level-up or be willing to go back in and modify the feat to account for increased damage as the character levels up.

Welcome to DDB homebrew.  I'm so sorry.

Thank you.