Click on the health bar.

And you apparently have to do that from the front side of the character and again click the health bar to exit from adjusting the max.

I have tried this and keep getting this error
Error in Script (Cragheart - 31034b) function <onClick>: chunk_3:(105, 12-69): cannot access field of user data <LuaGlobalPlayer><2>

Have the same "cannot access field of user data". It seems to work on a fresh game, but when I box up the character from an old load, save it as an object, open the object in a fresh game, try to raise max HP... I get the same error

I'm having this problem too. 2 characters both increased in level, it's recorded everywhere we can in the set up and we've tried changing the state of the base health next to the scenario xp counter but nothing seems to work. Anyone with anything more explanatory than "Click on the health bar" want to help?

There should be a health bar floating above your character's standee. If you click on that health bar, buttons to raise and lower your max hp should appear.

This is also the same method you can use to toggle a monster's normal/elite status. It also can be used to change a monster's hp (a few scenarios modify monsters and it's not scripted)

Thank you very much @Trequetrum, that nailed it! I didn't know those could be selected. This workshop build is incredible!