When you have enough XP to go to 11th level, the book says that you can "change entirely to a new class."
The book says this about what that means (in this section, under "Beyond 10th Level"):
Changing classes means keeping your ability scores, race, HP, and whatever moves you and the GM agree are core to who your character is. You lose all other class moves, replacing them with the starting moves of your new class.
Based on this, I wouldn't get the base HP of the new class, keeping my old HP instead.
However, I'm not sure whether I keep the damage die of my original class or take the damage die of my new class?
Here's some more context about the damage die, from the same page linked above (under "Damage"):
If a move just says “deal damage” the character rolls their class’s damage dice plus any bonuses or penalties from moves, weapons, or effects. (emphasis mine)
So, maybe another way to ask this question could be, when you deal damage after changing entirely to a new class after 10th level, do you roll the damage die of your original class or your new class?
Official sources, such as comments from the developers or quotes from the book, would be appreciated in an answer.