Preheat the oven to 400°F. Prepare a baking sheet with parchment paper.
In a large skillet, melt butter over medium-high heat. Add apples, brown sugar, sugar, lemon juice, cinnamon, and nutmeg. Toss together, reduce heat, cover, and cook until apples are tender, stirring occasionally, for 15 to 20 minutes. Remove from heat and cool.
Roll out the dough of either a prepared pie crust or my Homemade Pie Crust Recipe out on parchment paper to a 14 inch circle. Arrange apples in the center of the dough, leaving about 2 inches around the edge.
Fold the dough over the edge of the apples and press gently where the dough creases to seal. Brush the crust with water and sprinkle with the granulated sugar.