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.

Use the cutting board like a pizza peel. Open the oven, pull the rack out several inches, and carefully slide the foil and pizza onto the flat, preheated underside of the rimmed baking sheet. Bake for 13 to 15 minutes, until the crust is deeply golden at the edges and underneath, the mozzarella is completely melted with browned spots, and the squash is tender when pierced.

Using dry oven mitts, keep the baking sheet level as you remove it to a heatproof trivet. Use tongs and a wide spatula to transfer the pizza from the foil to the cutting board. Scatter the crisp sage over the pizza, completing the topping order. Rest for 5 minutes before cutting into 8 slices.