Preheat oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with parchment paper.
Combine flour, 1 cup butter, 3/4 cup white sugar, egg, baking powder, and 1/2 teaspoon salt in a food processor; pulse until crumbled and easily formed into dough when pinched. Pour 3/4 of the dough into the prepared pan; press down with your hands until crust is even and well packed.
Melt 3 tablespoons butter in a skillet over medium heat. Add apples, brown sugar, 1/2 cup white sugar, cinnamon, nutmeg, and salt; cook and stir until apples are softened, about 5 minutes. Stir in cornstarch; mix, adding more cornstarch if needed, until liquids are thickened.
Pour apple mixture onto crust; smooth with a spatula until even. Crumble remaining dough on top.
Bake in the preheated oven until crumbles on top are lightly brown, 30 to 40 minutes. Let cool for 10 minutes; cut into bars.