Crust 2 1/2 cups all-purpose flour, plus more for dusting 1 teaspoon sugar 1/2 teaspoon salt 14 tablespoons (1 3/4 sticks) cold unsalted butter, cut into small pieces 4 ounces sharp cheddar cheese, coarsely grated (about 1 1/2 cups) 1/2 cup ice water 1. Process flour, sugar, and salt in food processor. Add butter; pulse until pea-size lumps appear. Pulse in cheese. With processor running, add ice water; process just until dough comes together.
2. Wrap dough in plastic wrap and refrigerate until cold (at least 30 minutes or up to two days).
Filling 3/4 pound (about 2) Granny Smith apples, peeled, cored, and cut into small cubes 1 pounds (about 3) Cortland apples, peeled, cored, and cut into small cubes 1/4 cup white sugar 1/4 cup dark brown sugar 1/4 cup all-purpose flour 1 teaspoons fresh lemon juice 1/2 teaspoon ground cinnamon 1/8 teaspoon freshly grated nutmeg 1/8 teaspoon salt dash of ground cloves 1 tablespoons unsalted butter, cut into small pieces 1 egg yolk beaten with 2 tablespoons of water turbinado or regular granulated sugar for dusting 1. Preheat oven to 450 degrees. Divide dough into two pieces. On a lightly floured work surface, roll out one half of the dough to 1/8-inch thickness. Using a 4 1/2-inch-round cutter (something about the size of a martini glass) cut five to seven circles out of the rolled dough. Transfer the circles to a parchment-lined baking sheet, and place in the refrigerator to chill for about 30 minutes. Repeat the rolling, cutting, and chilling process with the remaining half of dough. 2. To make filling: Stir together apples, sugars, flour, lemon juice, and spices. 3. Remove the chilled dough from the refrigerator. Spoon about 1 to 2 tablespoons of filling onto one half of each circle of dough. Using your finger, brush a little cold water around the circumference of the dough. Fold the circle in half so the unfilled side comes over the filling, creating a semicircle. Seal the hand pie, and make a decorative edge by pressing the edges of the dough together with the back of a fork. Repeat process with remaining dough. Place the hand pies back on the parchment-lined baking sheet, and return to the refrigerator to chill for another 30 minutes. 4. Remove the chilled hand pies from the refrigerator, cut a small slit in each and lightly brush with the egg yolk wash. Sprinkle a pinch of the sugar lightly over the pies, and place pies in the oven to bake. Bake pie 10 minutes. Reduce oven temperature to 350ºF. Bake until the hand pies are golden brown, about 20 minutes. Remove the pies from the oven, and let stand to cool slightly before serving. Serve with vanilla ice cream, if desired.