Preheat your oven to 350°F (175°C). Roll out one pie crust and place it into a 9-inch baking dish. Sprinkle a layer of cinnamon and granulated sugar over the crust and rub it in. Bake for about 10 minutes until just set, then let it cool slightly.

In a saucepan, melt 4 tablespoons of butter over medium heat. Add 4 cups of frozen peaches and stir. Simmer for about 5 minutes until softened. Stir in lemon juice, vanilla extract, granulated sugar, brown sugar, cinnamon, and nutmeg. Continue simmering for an additional 10 minutes until bubbly.

Pour the peach mixture into the pre-baked crust. Cut the second pie crust into strips to create a lattice pattern over the peach filling. Sprinkle additional cinnamon and sugar on top.

Place the cobbler in the preheated oven and bake for 50 minutes until the crust is golden brown and the filling is bubbly.

Remove the cobbler from the oven and let it cool for at least 20 minutes to help the filling set.