Preheat the oven to 500°F with a pizza stone or upside-down baking sheet inside.
Whisk pumpkin puree, heavy cream, 1 tbsp olive oil, garlic, sage, cinnamon, nutmeg, salt, and pepper until smooth.
Dust a sheet of parchment with cornmeal. Stretch the dough into a roughly 12-inch round.
Spread the pumpkin mixture over the dough, leaving a 1-inch border for the crust.
Scatter Gouda and mozzarella evenly. Top with red onion and a light sprinkle of red pepper flakes, if using.
Brush the exposed crust edge with the remaining olive oil.
Slide the pizza (on parchment) onto the hot stone. Bake 12–15 minutes until the crust is deep golden and cheese bubbles.
Drizzle with balsamic glaze and top with arugula. Slice and serve hot.