Preheat the oven to 350 F. Lightly grease an 8 or 9-inch baking dish (circle or square). Set aside.

In a large bowl, combine peaches flour, sugar, salt, vanilla. Toss gently to combine, then pour into prepared baking dish, spreading the peaches evenly. Set aside.

In a medium mixing bowl, whisk together brown sugar, flour, oats, cinnamon, nutmeg and salt together. Add the butter and stir with a wooden spoon to break up the butter until the mixture is crumbly. (A fork or pastry cutter will work, too.) Sprinkle the oat topping evenly over the peaches.

Bake uncovered for 40-45 minutes until the topping is golden brown and the juices are bubbly around the edges. Transfer to a wire rack. Allow to cool slightly before serving.

Serve warm, room temperature, or cold. Cover leftovers tightly with foil or plastic wrap and store in the refrigerator for up to 5 days.