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 sliced peaches, granulated sugar, flour, cinnamon, nutmeg, lemon juice, and salt. Toss thoroughly until all peach slices are evenly coated with the spice mixture. Transfer the peach 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 ingredients. Using your fingers or a pastry cutter, work the butter into the mixture until it forms coarse, pea-sized crumbs. The mixture should hold together when squeezed but remain crumbly.
04 - Sprinkle the crumble topping evenly over the peach filling, covering completely. Bake for 35 minutes until the topping is golden brown and the fruit filling is bubbling around the edges.
05 - Remove from the oven and let the crumble cool for at least 10 minutes before serving. This allows the filling to set slightly. Serve warm with vanilla ice cream or whipped cream if desired.