Combine oat flour, baking powder, salt and rosemary in a large bowl. Mix in eggs, honey, water and olive oil until dough forms.
Turn the dough out onto a 12-inch pizza pan coated with cooking spray and spread it out with a large spoon or spatula. There will be one-inch space between the edge of the pizza and the edges of the pan.
Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add onions, season with salt and pepper, and sauté for 5-7 minutes, stirring occasionally. Remove to a bowl and reserve.
Add mushrooms to the skillet and cook until brown and soft, about 3-5 minutes. Stir in thyme.
To assemble the pizza, sprinkle mozzarella cheese and then the parmesan over the dough. Top with onions and then mushrooms (really load ‘em up!).
Transfer pizza to oven and cook for 15 minutes. Remove and drizzle with a little extra olive oil if desired. Enjoy with a fork—it will be a little crumbly.