Preheat oven to 425°F (220°C). Melt butter in a saucepan over medium heat and cook until golden brown and nutty, about 3–4 minutes.
In a large bowl, toss peaches with both sugars, lemon juice, vanilla, cinnamon, nutmeg, and cornstarch. Add browned butter and stir gently.
Press one pie crust into a 9-inch pie dish or skillet, covering the bottom and sides.
Pour in the peach mixture. Add optional crust pieces or crumble topping if using.
Place the second crust over filling, seal edges, and cut slits for steam.
Bake for 30–35 minutes until crust is golden and filling bubbles. If using crumble, add during the last 10 minutes.
Cool slightly before slicing. Serve warm with whipped cream or ice cream.