Prepare the Peaches
Preheat your oven to 350°F (175°C). Lightly grease a 9-inch baking dish with butter or nonstick spray.

In a large mixing bowl, toss the peach slices with granulated sugar, lemon juice, vanilla extract, cornstarch, cinnamon, and nutmeg. Stir gently until the peaches are well-coated and slightly glossy. Transfer the mixture into the prepared baking dish, spreading it evenly.

Make the Crumble Topping
In a separate bowl, combine the flour, oats, brown sugar, cinnamon, and salt. Add the cold butter cubes, and using your fingertips or a pastry cutter, work the butter into the dry ingredients until the mixture resembles coarse crumbs. The texture should be crumbly but hold together when pressed lightly.

Assemble and Bake
Evenly sprinkle the crumble topping over the peach filling, ensuring the fruit is mostly covered. Bake for 40-45 minutes, or until the top is golden brown and the peach juices are bubbling around the edges.

Serve and Enjoy
Let the crumble cool slightly before serving to allow the juices to thicken. Enjoy warm with a scoop of vanilla ice cream or a drizzle of heavy cream for an irresistible finish.