1 1/2 cups all-purpose flour
3/4 teaspoon kosher salt, divided
1/2 cup plus 2 teaspoons olive oil, divided
2 tablespoons ice water
1 tablespoon apple cider vinegar
1 medium butternut squash (about 2 pounds)
1 cup ricotta cheese
1/4 cup grated Pecorino Romano cheese
2 tablespoons finely chopped fresh sage leaves
2 cloves garlic, minced
1 large egg
Freshly ground black pepper
Arrange a rack in the middle of the oven and heat to 425°F.
Stir together the flour and 1/2 teaspoon salt in a large bowl. Add the 1/2 cup of the oil, water, and vinegar and mix gently with a fork, just enough to combine everything into a rough, crumbly dough.
Transfer the dough to a 9-inch tart pan and press it evenly over the entire bottom and up the sides of the pan. Prick it all over with a fork, line it with parchment paper or aluminum foil, and fill with pie weights.
Bake until the edges just start to brown, 12 to 15 minutes. Remove the weights and lining, and bake for another 5 minutes. Remove from the oven and reduce the oven temperature to 350°F.
Cut the top neck off the butternut squash. Wrap up the bottom tightly in plastic wrap and reserve in the refrigerator for up to 3 days for another use. Cut off the stem, peel the neck, and use a vegetable peeler to shave the flesh into long ribbons that are about 1-inch wide.
Mix the ricotta, Pecorino, sage, garlic, and egg in a medium bowl. Season with the remaining 1/4 teaspoon salt and a few grinds of pepper. Spread the ricotta mixture evenly over the bottom of the tart crust.
Roll each squash ribbon up tightly to form "roses" and place on top of the ricotta filling so that you see the coils, pressing down gently so that they stick. Continue with all of the ribbons or until you've completely covered the filling, whichever comes first.
Brush the tops of the roses with the remaining 2 teaspoons olive oil. Bake, loosely covered with aluminum foil, for 30 minutes. Uncover, increase the heat to 425°F, and bake until the roses are lightly browned on top, 20 to 30 minutes more.