Caramelize Onions: Heat olive oil in a large skillet over medium heat. Add onions and cook, stirring occasionally, for 7 to 8 minutes, until soft. Reduce heat to low and continue cooking until onions are blonde-colored, about 20 to 30 minutes. In the final 5 minutes, stir in garlic, salt, and red pepper flakes if using.
Prepare Pizza: Preheat oven to 475°F with a rack in the center-top position. Place a pizza stone or baking sheet on the rack. On a flour-coated surface, roll out dough to a 12 to 14-inch round, then transfer to parchment paper. Pierce the dough a few times with a fork. Spread pumpkin puree over dough, leaving a 1/2-inch border. Top evenly with caramelized onion mixture and gouda cheese.
Bake on the preheated stone or baking sheet for about 12 minutes, or until the crust is crisp and cheese is melted. Garnish with parsley before serving if desired.