Preheat your oven to 375°F and lightly spray the inside of a pie pan with non-stick cooking spray.
In a food processor, crush the snickerdoodle cookies into coarse crumbs with a few larger chunks for texture.
Mix the cookie crumbs with 4 tablespoons of brown sugar, then pour in melted butter and combine with a fork until it resembles damp sand.
Press most of the crumb mixture into the pie pan to form an even crust. Reserve 1 cup of crumb mixture for the topping.
In a large skillet, melt the butter for the filling over medium heat. Add the sliced apples and 2 tablespoons of brown sugar. Stir, cover, and cook for 10-12 minutes until the apples begin to soften.
Sprinkle the flour, cinnamon, and nutmeg over the cooked apples and stir to incorporate. Continue to cook until the mixture thickens slightly, then remove from heat.
Pour the apple mixture into the prepared crust, spread it evenly, and top with the reserved crumb mixture.
Bake the pie at 375°F for 18 minutes, or until the crust is golden brown and the filling is bubbling.
Let the pie cool for at least 15 minutes before serving. Enjoy warm or at room temperature!