Preheat your oven to 375°F (190°C). Lightly grease a baking dish with butter or non-stick spray.
Slice the peaches into thin, even wedges, removing the pits. Place them in a mixing bowl and toss with sugar, cinnamon, and salt until evenly coated.
Spread the sugared peaches evenly in the prepared baking dish, creating a level layer with no gaps.
In a separate bowl, combine flour, oats, and brown sugar. Add the cold, cubed butter.
Use a pastry cutter or fork to cut the butter into the dry ingredients until the mixture resembles coarse crumbs with some larger pea-sized pieces.
Sprinkle the crumble mixture evenly over the peaches, covering the filling completely.
Bake in the preheated oven for about 30 minutes, or until the topping turns golden brown and the filling bubbles around the edges.
Remove the crumble from the oven and let it sit for a few minutes to set slightly. Serve warm, optionally with a scoop of vanilla ice cream.