Step 1: Preheat your oven to 375°F (190°C). Grease a 9-inch pie dish or an 8x8-inch baking dish.
Step 2: In a large bowl, gently combine the fresh or thawed and drained mulberries with 1/2 cup granulated sugar, cornstarch, lemon juice, and lemon zest. Pour the fruit mixture into your prepared baking dish.
Step 3: In a separate medium bowl, combine the all-purpose flour, rolled oats, brown sugar, 1/4 cup granulated sugar, and salt. Whisk these dry ingredients together.
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: Evenly sprinkle the crumble topping over the mulberry mixture in the baking dish.
Step 6: Place the baking dish on a baking sheet and bake in the preheated oven for 35-45 minutes, or until the topping is golden brown and the fruit filling is bubbly and tender.
Step 7: Carefully remove the crumble from the oven and let it cool on a wire rack for at least 15-20 minutes before serving. This allows the filling to set properly.