Add the raspberries to a blender or food processor and pulse until smooth. Pour the puree into a metal sifter in batches, pushing it through to remove the seeds. This step is optional but recommended for a smooth texture. Pour the seedless puree into a small saucepan over low-medium heat. Simmer gently, stirring occasionally, to reduce the puree and remove excess liquid. Continue until the puree is thickened and you have about 1/4 to 1/3 cup, which should take around 15-20 minutes. Remove from heat and let the thickened raspberry puree cool as you continue with the recipe.

Preheat your oven to 325°F (160°C). Line a 9x13 inch (23x33 cm) baking pan with parchment paper, leaving an overhang for easy removal later. In a medium bowl, whisk together the all-purpose flour, white sugar, 1 tablespoon cornstarch, and salt. Stir in the melted butter until the mixture is thick. Press the dough evenly into the bottom of the prepared pan, creating a slight lip around the edge. Bake in the preheated oven for 20-25 minutes, or until the top is set and slightly golden. Once baked, remove from oven and gently prick the top with a fork—don't go all the way through. As a personal tip, I like to let the base cool just until it's no longer steaming to help the topping set evenly.

While the base is baking, make the filling. In a large bowl, whisk together the granulated sugar and 1/3 cup cornstarch until there are no lumps. Whisk in the eggs, one at a time, until fully incorporated. Add the cooled, thickened raspberry puree from Step 1, whisking until evenly combined. Gradually whisk in the lemon juice. The mixture should be quite liquid — that's normal for bars like these.

Pour the lemon raspberry mixture from Step 3 evenly over the still-warm shortbread base from Step 2. Return the pan to the oven (still at 325°F/160°C) and bake for 20-25 minutes, or until the top is set and doesn’t jiggle when you shake the pan gently. Remove from the oven and let the bars cool in the pan for at least 1 hour, or until they reach room temperature. I like to chill them overnight for the cleanest slices and best flavor, but a minimum of 2 hours in the fridge works well.

Once fully chilled, use the parchment paper overhang to lift the bars out of the pan. Place on a cutting board, and slice into bars with a sharp knife. For clean, neat slices, wipe the blade between cuts. Store the bars in the refrigerator. For a bright touch, I like to sprinkle a bit of powdered sugar or extra raspberries on top just before serving, though that's completely optional.