Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper.

Combine flour, 1 cup butter, ¾ cup white sugar, egg, baking powder, and ½ teaspoon salt in a food processor; pulse until crumbled and easily formed into dough. Press ¾ of the dough into the prepared pan to form an even crust.

Melt 3 tablespoons butter in a skillet over medium heat. Add apples, brown sugar, white sugar, cinnamon, nutmeg, and pinch of salt. Cook until apples soften (about 5 minutes). Stir in cornstarch until thickened.

Pour caramel-apple mixture onto the crust and smooth with a spatula. Crumble remaining dough on top.