For the sauce, place a medium saucepan over median-high heat with 1 tablespoons olive oil. Once hot, add the onions and garlic and cook until softened, about 5 minutes. Stir in the cherry tomatoes, cooking until the tomatoes have blistered, another 5 minutes. Add the pumpkin purée and water, and stir until fully combined. Season with salt, pepper, red pepper flakes, and bring to a simmer. Lower the flame and cook until slightly reduced, about 10 minutes. Remove from heat and let cool slightly.
To prepare the pizza toppings, set a skillet over medium-high heat with 1 tablespoon olive oil. Once hot, add the chorizo and cook until brown and crispy, about 5 minutes. Stir in the sliced mushrooms, cooking until also browned, another 5 minutes. Remove from heat.
Preheat oven to 475 degrees F. Sprinkle a pizza stone, pizza pan, or baking sheet with cornmeal, set aside.
Roll the dough out on a lightly floured work surface into about a 1/2-inch thick round circle. Transfer the dough to the prepared pizza stone (or baking pan or baking sheet), and fold the very edge over the top of the pizza to create a thick crust. Spread the center evenly with the pumpkin pizza sauce. Sprinkle with mozzarella, fontina and parmesan cheese. Top with the sautéed chorizo, mushrooms and sage leaves. Bake until puffed up, the cheese has melted, and the pizza is golden brown, about 15 to 20 minutes.
Remove from the oven and let cool slightly. Top with arugula and pumpkin seeds right before cutting and serving. Enjoy!