01 - Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving a slight overhang for easy removal of the bars later.
02 - Combine flour, granulated sugar, and salt in a medium bowl. Cut in the cold butter using a pastry blender or fork until the mixture resembles coarse crumbs.
03 - Press the crumb mixture firmly into the bottom of the prepared pan. Bake for 15 to 18 minutes, or until lightly golden.
04 - While the crust bakes, whisk together sugar, flour, and baking powder in a bowl. Add eggs, lemon juice, and lemon zest, whisking until completely smooth.
05 - Gently fold the fresh raspberries into the lemon mixture, being careful not to crush them excessively.
06 - Pour the lemon raspberry mixture evenly over the warm crust. Return to the oven and bake for 22 to 25 minutes, until the center is completely set and no longer jiggles when gently shaken.
07 - Remove from the oven and allow the bars to cool completely in the pan. For cleanest cuts, refrigerate for 1 to 2 hours until fully chilled before slicing.
08 - Dust the cooled bars with powdered sugar just before serving, if desired. Cut into 12 even bars and serve chilled or at room temperature.