Parmesan Custard Tart with Butternut Squash

Name: Parmesan Custard Tart with Butternut Squash
Ingredients: 1 1/4 cups all-purpose flour; 2 1/2 teaspoons finely chopped fresh sage; Rounded 1/4 teaspoon salt; 3/4 stick (6 tablespoons) cold unsalted butter, cut into cubes; 2 tablespoons cold vegetable shortening, cut into pieces; 2 to 4 tablespoons ice water; 1 large egg white (yolk reserved for filling), lightly beaten; 2 ounces finely grated Parmigiano-Reggiano (1 cup); 1 cup heavy cream; 1 1/2 tablespoons olive oil; 3/4 pound piece butternut squash, peeled, seeded, and cut into 1/2-inch pieces (2 cups); 3/8 teaspoon salt; 1/4 teaspoon coarsely ground black pepper; 1 whole large egg; 1 large egg yolk; Garnish: fried sage leaves; a pastry or bench scraper; a 13 1/2- by 4-inch rectangular* or 8 1/2-inch round fluted tart pan with a removable bottom; pie weights or raw rice