Preheat your oven to 375°F (190°C) and lightly grease a baking dish.
In a mixing bowl, gently toss the sliced peaches with half of the sugar and vanilla extract until evenly coated. Spread the fruit mixture into the prepared baking dish.
In another bowl, combine the flour, oats, remaining sugar, and cinnamon. Add the cold butter pieces and use your fingers or a pastry cutter to mix until the crumble resembles coarse crumbs, with some larger pea-sized pieces.
Sprinkle the crumble topping evenly over the peaches, covering them completely with a textured, golden layer.
Bake in the oven for about 40 minutes, or until the topping is crisp and golden and the filling is bubbling around the edges. The aroma of baked peaches and toasted oats will fill the kitchen.
Remove from the oven and let it cool slightly. Serve warm, preferably with a scoop of vanilla ice cream or a dollop of cream for an extra treat.