If using fresh peaches, sprinkle the sugar, flour, and nutmeg over the peaches and stir to coat. Let rest for about 30 minutes, until softened. If using frozen peaches, proceed to the next step.
Preheat your oven to 475°F.
Add the peaches (with the sugar, flour, and nutmeg) into a large skillet over medium-high heat. Bring to a boil and then let simmer for 15 minutes over low heat. Remove from heat and stir in the butter and vanilla extract. Stir until the butter has completely melted.
On a lightly floured surface, roll out the first pie dough to a 10"x10" square. Use a pastry cutter, pizza cutter, or knife to form straight edges. Save the excess dough.
In a lightly greased 10"x10" baking dish, add half of the peach mixture. Carefully place the square pie dough over the top of the dough. Bake for 12 minutes until the dough is lightly browned.
Meanwhile, roll out the second pie dough to a 10"x10" square. Cut into 8 strips.
Remove the dish from the oven and ladle the remaining peach filling over the center crust. Arrange the strips of dough into a lattice design over the top of the peaches (see blog post and/or video for details on how to do this). Pinch pieces of the leftover dough and insert them all throughout the top layer of filling.
Make an egg wash by combining the egg with 1 tbsp of water in a small bowl. Brush the egg wash all over the strips of dough. Sprinkle the turbinado over the dough.
Bake for another 15 to 18 minutes, until the top is nicely browned and the filling is bubbly. Let rest for 5 to 15 minutes before serving. Serve with vanilla ice cream, if desired.