Prepare Oven and Pan: Preheat your oven to 350°F (175°C). Lightly grease or spray a 9×13 inch baking dish to prevent sticking and set aside.
Combine Dry Ingredients: In a food processor, add the all-purpose flour, almond flour, 1 cup sugar, baking powder, and salt. Pulse a few times to evenly mix these dry ingredients.
Incorporate Butter and Flavor: Add the cold butter cubes, egg, and almond extract to the dry mix in the food processor. Pulse in short bursts until the mixture resembles coarse crumbs and starts to come together into a loose dough. It will still look crumbly but should hold when pressed.
Form the Base Layer: Remove about two-thirds of the dough from the processor and scatter it evenly across the bottom of the prepared baking pan. Using the back of a measuring cup or your fingers, gently press the dough down to create a uniform crust layer without packing it too tightly. Smooth the surface with an offset spatula for an even finish.
Prepare the Raspberry Filling: Place rinsed raspberries and ⅓ cup sugar in a medium saucepan. Heat over medium heat, stirring frequently, until the raspberries begin to break down and release their juices. Add a splash of water if the fruit sticks to the pan. Once boiling, reduce heat to low and simmer, mashing the berries with a spoon until the mixture is thick and saucy.
Thicken the Filling: In a small bowl, whisk cornstarch with a few teaspoons of cold water until smooth. Slowly stir this slurry into the simmering raspberry mixture. Bring back to a gentle boil and cook for another 1-2 minutes until the sauce thickens noticeably. Remove from heat and let cool completely before use.
Assemble the Bars: Spread a generous layer of the cooled raspberry filling evenly over the dough crust in the pan. Crumble the remaining dough over the filling, distributing it loosely to cover. Sprinkle sliced almonds evenly across the top.
Add Final Touch and Bake: Lightly sprinkle 1 teaspoon of granulated sugar over the almond topping to encourage a subtle caramelized finish. Bake in the preheated oven for about 30 minutes, or until the edges are golden and the topping is set but still slightly soft.
Cool and Serve: Allow the bars to cool fully in the pan on a wire rack. Once cooled, slice into 20 squares and serve. Store leftovers in an airtight container in the refrigerator.