Preheat the oven to 425. Wrap the head of garlic in foil and roast for about 20-30 minutes, this can be done an advance and cooled.
Bring the pizza dough up to room temperature or whatever else is required by the directions.
Meanwhile, cut the end off of the delicata enough that you can reach a spoon into the center. Scrape the seeds out with a spoon as far in as possible. Thinly slice the delicata into paper thin pieces.
Cut the stem off the top of the persimmon. Thinly cut the persimmon into paper thin slices.
Bring the cream cheese up to room temperature and peel the proscuitto into torn up pieces.
Squeeze the roasted garlic out and place in a small bowl. Whisk in the olive oil with a pinch of salt and black pepper, smashing together to create a paste-like mess.
Spread the pizza dough onto a pizza stone or baking sheet. Drizzle and rub around the garlic-olive oil. Top with the shredded cheese, delicata + persimmon slices, dollops of cream cheese, and prosciutto pieces.
Bake for 8-15 minutes until cooked through with golden crust edges and gooey-melted cheese. Finish with the fresh thyme or minced sage if using.