Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving overhang on two sides for easy removal later.

Make the shortbread crust by combining 2 cups flour, 1/2 cup powdered sugar, salt, and 1 tablespoon lemon zest in a large bowl. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.

Press the crust mixture firmly and evenly into the bottom of the prepared pan. Bake for 18-20 minutes until the edges are lightly golden. The center may look slightly underdone but will continue baking with the filling.

While the crust bakes, whisk together the eggs and granulated sugar in a medium bowl until smooth and slightly thickened, about 1 minute.

Add the lemon juice, remaining tablespoon of lemon zest, 3 tablespoons flour, and baking powder to the egg mixture. Whisk until completely smooth with no lumps.

Remove the hot crust from the oven and immediately pour the lemon filling over it, spreading gently to the edges if needed.

Return the pan to the oven and bake for 22-25 minutes until the filling is set around the edges but still jiggles slightly in the center when you gently shake the pan.

Cool completely on a wire rack at room temperature for 1 hour, then refrigerate for at least 2 hours until fully chilled and set.

Use the parchment overhang to lift the bars out of the pan. Cut into 16 squares with a sharp knife, wiping clean between cuts. Dust generously with powdered sugar just before serving.