Preheat your oven to 375°F (190°C) and lightly grease your baking dish to prevent sticking.
In a large bowl, toss the sliced peaches with granulated sugar, ground cinnamon, and vanilla extract until evenly coated. The peaches should look glossy and fragrant.
Pour the peach mixture into your prepared baking dish, spreading it out into an even layer. The peaches should form a juicy, bubbling base when baked.
In a separate bowl, combine the flour, rolled oats, brown sugar, and salt. Mix until well combined.
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 look crumbly but hold together when pressed.
Sprinkle the crumble topping evenly over the peaches, covering the fruit completely. The topping should be generous and textured.
Bake in the preheated oven for about 35-40 minutes, or until the topping is golden brown and the filling is bubbling around the edges.
Remove the crumble from the oven and let it cool slightly. The aroma of cinnamon and baked peaches will fill the room as it cools.
Serve warm, ideally with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.