Preheat the oven to 350 degrees Fahrenheit.
In a mixing bowl, add the sliced and peeled peaches. Add the white sugar, brown sugar, vanilla, lemon juice, cornstarch, cinnamon and nutmeg all at once.
Mix these ingredients with the peaches, coating them completely in this sticky mixture.
Pour this into the baking dish and bake for 5 minutes.
While that bakes, make the crumble topping. In a separate mixing bowl, add the flour, baking powder, white sugar, and brown sugar. Whisk together until combined.
Then add the softened butter and vanilla. Use a pastry cutter or fork to blend the butter into the dry ingredients until a crumbly mixture forms.
Take the peaches out of the oven and top with the crumble topping, almost leaving no peaches uncovered.
Place back in the oven and bake for another 25 minutes. If desired, turn the oven on and broil for about 3 minutes before the peach cobbler is done to brown the topping a bit more.
Remove from the oven and let cool for about 5 minutes. Then, Top with ice cream, serve, and enjoy!