Preheat oven to 350°F (175°C). Line an 8x8 inch baking pan with parchment paper, leaving an overhang on two sides for easy removal. In a medium bowl, combine flour, sugar, and salt. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs. Press firmly and evenly into the bottom of the prepared pan. Bake for 15-18 minutes, or until lightly golden. Remove from oven and let cool slightly.

While the crust bakes, whisk together the eggs and sugar in a large bowl until smooth and slightly thickened. Whisk in the fresh lemon juice and lemon zest. In a separate small bowl, whisk together the 1/4 cup flour and baking powder, then gently fold this into the wet egg mixture until just combined.

Gently fold the 1 cup of fresh raspberries into the lemon filling. Pour the filling over the warm crust, spreading it evenly. Bake for 25-30 minutes, or until the filling is set and the edges are lightly golden. The center should have a slight jiggle.

Place the pan on a wire rack and allow the bars to cool completely in the pan, about 1 hour. Then, refrigerate for at least 2 hours (or overnight) to fully set. This makes for clean cuts.

Using the parchment paper overhang, lift the entire slab of bars out of the pan. Place on a cutting board. Using a sharp knife dipped in hot water and wiped dry between cuts, slice into 16 squares. Dust with powdered sugar if desired. Serve plain, or top individual bars with a dollop of whipped cream and a fresh raspberry.