Step 1: Preheat your oven to 375°F (190°C). Lightly grease an 8x8 inch or 9x9 inch baking dish.
Step 2: In a large bowl, gently combine the blackberries, granulated sugar, cornstarch (or flour), lemon juice, and a pinch of salt. Toss until the berries are evenly coated. Pour this fruit mixture into your prepared baking dish.
Step 3: In a separate medium bowl, combine the rolled oats, all-purpose flour, light brown sugar, and ground cinnamon. Whisk these dry ingredients together until well combined.
Step 4: Add the cold, diced unsalted butter to the dry ingredients. Using your fingertips, a pastry blender, or two knives, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 5: Sprinkle the oat crumble mixture evenly over the blackberry filling in the baking dish.
Step 6: Place the baking dish on a baking sheet and bake in the preheated oven for 40-50 minutes, or until the topping is golden brown and the filling is bubbly around the edges. If the topping browns too quickly, loosely tent with foil.
Step 7: Remove from the oven and let cool for at least 15-20 minutes before serving. This allows the filling to set and prevents it from being too runny.