Prepare your baking pan by lining a 9×9-inch square baking pan with parchment paper, leaving overhang on the sides for easy removal later. Preheat your oven to 350°F (175°C).
Make the shortbread crust by combining flour, sugar, and salt in a food processor. Add cold butter cubes and vanilla, then pulse until the mixture resembles coarse crumbs that hold together when pressed.
Press the crust mixture firmly into the bottom of your prepared pan, creating an even layer. Use the bottom of a measuring cup to ensure it’s packed tightly and evenly.
Bake the crust for 15-18 minutes until it’s lightly golden around the edges. Remove from oven but keep the oven on.
Prepare the raspberry swirl while the crust bakes by blending raspberries, sugar, and lemon juice in a blender or food processor until smooth. Strain through a fine-mesh sieve to remove seeds, pressing with a spoon to extract all the juice.
Make the lemon filling by whisking eggs and sugar together until light and well combined. Add lemon juice and zest, then whisk in flour, baking powder, and salt until the mixture is smooth with no lumps.
Pour the lemon filling over the pre-baked crust while it’s still warm.
Create the raspberry swirl by dropping small spoonfuls of the raspberry puree over the lemon filling. Use a toothpick or skewer to gently swirl the raspberry into the lemon layer, creating a marbled effect.
Bake for 22-25 minutes until the filling is set but still has a slight jiggle in the center. It will continue to set as it cools.
Cool completely in the pan on a wire rack for at least 2 hours, then refrigerate for an additional hour to fully set.
Lift the bars from the pan using the parchment paper overhang, then cut into squares with a clean, sharp knife.
Dust with powdered sugar just before serving for a beautiful finishing touch.