Step 1: Preheat your oven to 375°F (190°C). Line an 8×8 or 9×9 inch baking pan with parchment paper, leaving an overhang on the sides.
Step 2: In a large bowl, combine the all-purpose flour, old-fashioned rolled oats, 1/2 cup granulated sugar, light brown sugar, baking powder, and salt. Whisk well.
Step 3: Add the cold, cubed unsalted butter to the dry ingredients. Cut the butter into the mixture using your fingertips, a pastry blender, or a food processor until coarse crumbs form.
Step 4: Reserve 1 cup of the crumb mixture for the topping. Press the remaining mixture firmly into the bottom of the prepared pan. Bake for 10-12 minutes, or until lightly golden.
Step 5: While the crust bakes, prepare the raspberry filling. In a medium bowl, gently combine the fresh or frozen raspberries, 1/4 cup granulated sugar, and cornstarch.
Step 6: Remove the partially baked crust from the oven. Evenly spread the raspberry filling over the warm crust.
Step 7: Sprinkle the reserved 1 cup of crumb mixture evenly over the raspberry filling.
Step 8: Return the pan to the oven and bake for an additional 25-30 minutes, or until the topping is golden brown and the filling is bubbly and set.
Step 9: Let the bars cool completely in the pan on a wire rack before lifting out and cutting into squares. Cooling completely is crucial for them to set properly. Store in an airtight container.