01 - Preheat the oven to 350°F. Lightly grease a 2-quart baking dish with butter or cooking spray.
02 - In a large mixing bowl, combine the peach slices, granulated sugar, flour, cinnamon, nutmeg, lemon juice, and salt. Toss thoroughly until the peaches are evenly coated with the seasoning mixture. Transfer the fruit mixture to the prepared baking dish and spread into an even layer.
03 - In a separate bowl, whisk together the flour, oats, brown sugar, cinnamon, and salt. Add the cold, cubed butter to the dry mixture. Using your fingers or a pastry cutter, work the butter into the dry ingredients until the mixture resembles coarse, pea-sized crumbs. The butter should remain slightly cold to ensure proper texture.
04 - Sprinkle the crumble topping evenly over the peach filling, covering the fruit completely. Gently press down on the topping to help it adhere.
05 - Bake for 35 minutes, or until the topping is golden brown and the fruit filling is bubbling around the edges. If the topping browns too quickly, tent loosely with aluminum foil during the last 5-10 minutes of baking.
06 - Allow the crumble to cool for at least 10 minutes before serving to let the filling set slightly. Serve warm while the topping remains crisp. Top with vanilla ice cream or whipped cream if desired.