Step 1: Preheat your oven to 375°F (190°C). Line a 9×13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a large bowl, whisk together 1 3/4 cups all-purpose flour (reserve 1/4 cup for later), 1/2 cup granulated sugar, and 1/4 teaspoon salt. Cut in 1 cup (2 sticks) softened unsalted butter using a pastry blender, two knives, or your fingertips, until the mixture resembles coarse crumbs.
Step 3: Remove 1 cup of this mixture and set aside – this will be your crumb topping. Stir 1/2 cup sliced almonds and 1/2 teaspoon almond extract into the reserved crumb mixture.
Step 4: Press the remaining flour mixture firmly and evenly into the bottom of the prepared baking pan. Bake for 15-18 minutes, or until lightly golden brown.
Step 5: While the crust is baking, prepare the raspberry filling. In a medium bowl, gently combine 4 cups fresh or frozen raspberries, 1/2 cup granulated sugar, 2 tablespoons all-purpose flour, 1 tablespoon lemon juice, and 1/2 teaspoon almond extract.
Step 6: Once the crust is lightly golden, remove it from the oven. Spread the raspberry filling evenly over the warm crust.
Step 7: Evenly sprinkle the reserved almond crumb topping over the raspberry filling.
Step 8: Return the pan to the oven and bake for another 30-35 minutes, or until the topping is golden brown and the raspberry filling is bubbly and set.
Step 9: Allow the bars to cool completely in the pan on a wire rack before cutting. This is essential for clean slices and for the filling to fully set. Once cooled, lift the bars out of the pan using the parchment paper overhang and cut into squares. Store leftovers in an airtight container.