Preheat your oven to 355°F (180°C). Line an 8×8-inch baking pan with parchment paper, allowing extra paper to hang over the edges for easy removal.
In a medium bowl, combine the sugar and lemon zest for the crust. Rub the zest into the sugar with your fingertips until fragrant.
Beat the softened butter with the lemon sugar until light and creamy. Add the vanilla extract and sea salt.
Gradually mix in the flour until a soft dough forms. Press the dough evenly into the prepared pan, creating a slight lip around the edges.
Bake the crust for 20–25 minutes or until lightly golden around the edges. Remove and let cool slightly.
Mash the raspberries thoroughly and strain through a fine-mesh sieve. You should have about ¼ cup smooth raspberry puree.
In a clean bowl, combine the sugar and lemon zest for the filling. Rub together until fragrant.
Whisk in the flour and salt.
Add the eggs, raspberry puree, and lemon juice. Stir gently until smooth. Avoid overmixing to maintain a silky texture.
Pour the Raspberry Lemon Bars filling over the partially cooled crust.
Tap the pan gently on the counter to remove any trapped air bubbles.
Bake for 17–20 minutes, or until the edges are set and the center has a slight jiggle.
Cool completely at room temperature for about 2 hours.
Refrigerate for at least 1 hour to fully set.
Lift the bars from the pan using the parchment paper. Dust with powdered sugar and slice before serving.