Step 1: Preheat your oven to 375°F (190°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides for easy lifting.
Step 2: In a large bowl, whisk together the all-purpose flour, rolled oats, 1/2 cup granulated sugar, 1/2 cup light brown sugar, baking powder, and salt.
Step 3: Add the cold, unsalted butter, cut into small cubes. Use a pastry blender, your fingertips, or a food processor to cut the butter into the dry ingredients until it resembles coarse crumbs. Some larger pea-sized pieces are fine.
Step 4: Press about two-thirds of the crumble mixture evenly into the bottom of the prepared baking pan. Reserve the remaining one-third for the topping.
Step 5: In a separate medium bowl, gently combine the fresh black raspberries with 1/4 cup granulated sugar, lemon juice, and cornstarch. Be gentle to avoid crushing the delicate berries.
Step 6: Spread the black raspberry filling evenly over the pressed crumble base in the baking pan.
Step 7: Sprinkle the remaining one-third of the crumble mixture over the black raspberry filling.
Step 8: Bake for 35-45 minutes, or until the topping is golden brown and the filling is bubbly.
Step 9: Allow the bars to cool completely in the pan on a wire rack before cutting into squares or rectangles. This is crucial for the bars to set properly.