Line an 8x8 or 9x9 square baking pan with parchment paper and set aside.
In a food processor, pulse together cups flour, powdered sugar, and salt. Add butter and pulse until it resembles cornmeal.
Pulse in egg until a soft, crumbly dough forms. Scoop dough into prepared pan and press evenly to cover bottom. Prick all over with a fork and chill in the freezer for 30 minutes.
Preheat oven to 375° while crust chills. Bake crust for 20-25 minutes, until golden. Let cool while you prepare the filling.
For filling
In a large sauté pan, melt tablespoons butter over medium-low heat. Add apples, granulated sugar, cinnamon, and vanilla and stir to coat. Cook until apples are softened, approximately 15 minutes.
Spoon apples evenly into baked crust, scraping the pan to collect caramelized juices.
For topping
To make the topping, in a food processor, pulse together flour, granulated sugar, brown sugar, and butter until coarse crumbs are formed. Scatter crumb over the top of the apples.
Bake at 375°F for 30-40 minutes, until golden brown. Let cool completely before cutting.
Notes
In place of the homemade filling, you can use one 20-ounce can or jar apple pie filling.
You can also make the crust and topping using a bowl and pastry blender instead of a food processor.