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 removal.
Step 2: In a large bowl, whisk together the flour, 1/2 cup granulated sugar, baking powder, and salt.
Step 3: Add the cold, cubed butter to the dry ingredients. Using your fingers, a pastry blender, or a stand mixer with a paddle attachment, cut the butter into the flour mixture until it resembles coarse crumbs. Some larger pea-sized pieces are fine.
Step 4: Press about two-thirds of this mixture evenly into the bottom of the prepared baking pan. Lightly press down to form a compact crust.
Step 5: In a medium bowl, gently toss the fresh or frozen raspberries with 1/4 cup granulated sugar, cornstarch, and lemon juice until the berries are evenly coated. Be gentle to avoid mashing the berries too much.
Step 6: Pour the raspberry mixture evenly over the pressed crust in the baking pan.
Step 7: Sprinkle the remaining one-third of the crumble mixture evenly over the raspberry filling.
Step 8: Bake for 40-45 minutes, or until the crumble topping is golden brown and the raspberry filling is bubbly and set.
Step 9: Remove from the oven and let the bars cool completely in the pan on a wire rack before cutting. This is essential for the filling to set properly and ensures clean cuts. If you cut them warm, they will likely fall apart. Store any leftovers in an airtight container at room temperature for up to 3 days, or in the refrigerator for up to a week.