Make pastry dough: Grate butter and cheese in a food processor fitted with large-hole grate disk or through the shredder side of a box grater. Transfer mixture to a bowl. Replace grater disk of food processor with a blade. Add flour, granulated sugar, salt, butter, and cheese to food processor; pulse until mixture resembles coarse crumbs. Add 8 tablespoons chilled water, pulsing until mixture just forms a dough, adding additional water, 1 tablespoon at a time, if dough is too dry (test by pressing some dough between fingertips to see if it holds together). Transfer dough to a lightly floured surface and knead slightly until dough just comes together. Form dough into a flat disk and wrap well in plastic wrap. Chill until firm, at least 1 hour or overnight (if chilling overnight, let stand at room temperature 10 minutes before rolling).

Preheat oven to 350 degree F. Butter sheet pan. Roll out dough on a lightly floured surface with a floured rolling pin into a 16-inch round. Brush excess flour from dough and transfer to prepared pan. Chill dough until firm, about 15 minutes.

Make filling: Meanwhile, toss apples with juice, cinnamon, granulated sugar, and flour in a large bowl until combined well.

Mound apple mixture in center of dough and bring up edges toward center, pleating dough to create a round tart. Brush top of dough with egg and sprinkle with sanding sugar. Bake tart in middle of oven until apples are tender and crust is golden brown, about 45 minutes.

In a small saucepan over moderately low heat, melt apricot preserves with 1 teaspoon water. Strain through a sieve into a bowl (discard solids). Brush apricot glaze over apples.

Cut tart into wedges and serve with vanilla ice cream. Makes 8 servings.