Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch baking dish or a similar sized casserole dish.

Prepare the fruit filling: In a large bowl, gently combine the raspberries, sliced peaches, granulated sugar, cornstarch, and lemon juice. Toss lightly until the fruit is evenly coated. Pour the mixture into the prepared baking dish and spread into an even layer.

Prepare the crumble topping: In a separate medium bowl, whisk together the flour, rolled oats, brown sugar, and ground cinnamon.

Cut in the butter: Add the cold, cubed butter to the dry ingredients. Use your fingertips, a pastry blender, or two knives to cut the butter into the flour mixture until it resembles coarse crumbs, with some pea-sized pieces of butter remaining.

Assemble and Bake: Sprinkle the crumble topping evenly over the fruit filling in the baking dish. Bake for 35 to 40 minutes, or until the topping is golden brown and the fruit filling is bubbly around the edges.

Cool slightly before serving. This crumble is best served warm, perhaps with a scoop of vanilla bean ice cream or a dollop of whipped cream.