Preheat your oven to 375°F (190°C). Peel, pit, and slice the peaches, then toss them with granulated sugar in a mixing bowl to enhance their natural sweetness.
Spread the sweetened peach slices evenly in the bottom of your baking dish, creating a smooth layer that will bake into a juicy filling.
In another bowl, combine the flour, oats (if using), brown sugar, and salt. Mix these dry ingredients together for the crumble topping.
Add the cold, cubed butter to the dry mixture. Use a pastry cutter or forks to cut in the butter until the mixture resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumble mixture evenly over the peaches, covering them completely to create a thick, layered topping.
Bake in the preheated oven for about 40 minutes, or until the topping is golden brown and the filling is bubbling around the edges.
Remove the crumble from the oven and let it cool slightly before serving. The topping will be crunchy and shatter easily, while the peaches inside stay warm and juicy.
