Butternut Squash, Sage, and Caramelized Onion Pizza

Remove the dough from the refrigerator and keep it covered at room temperature. Place the rimmed baking sheet upside down on a lower-middle oven rack and preheat the oven to 475°F for at least 30 minutes. Meanwhile, halve and peel the onion, then slice it 1/8 inch thick. Peel a firm section of the squash neck and use the vegetable peeler to shave 2 loosely packed cups of thin ribbons. Shred the mozzarella and grate the Parmesan. Keep the sage leaves whole and pat them completely dry.

Heat 1 tablespoon olive oil in the skillet over medium-high heat. Add the onion and 1/4 teaspoon salt. Cook for 4 minutes, stirring frequently. Add the water, reduce the heat to medium, and cook for 7 to 9 minutes, stirring often, until the onion is soft and deeply golden with browned edges. Transfer it to a bowl.

Return the skillet to medium heat and add 1 teaspoon olive oil. Add the dry sage leaves in a single layer and cook for 30 to 60 seconds, turning once, until slightly darkened and curled at the edges. Transfer to a plate; the leaves will become crisp as they cool.

Place the squash ribbons in the mixing bowl. Toss with 1 tablespoon olive oil, the remaining 1/2 teaspoon salt, and the black pepper, gently separating the ribbons.

Lay a 12-by-16-inch sheet of heavy-duty foil on the cutting board and brush its center with 1 teaspoon olive oil. Dust the dough and your hands with the flour. Press the dough outward, leaving a 1/2-inch border, then stretch it over your knuckles into a roughly 10-by-14-inch rectangle. Place it on the prepared foil and adjust the shape. If it springs back, let it rest for 5 minutes before finishing.

Brush the dough with the remaining 1 teaspoon olive oil. Add the toppings in this order: mozzarella, caramelized onion, squash ribbons arranged in loose folds with minimal overlap, and Parmesan. Reserve the fried sage until after baking.