Prepare Oven and Pan: Preheat your oven to 350°F (175°C). Line a 9x13-inch baking dish with parchment paper, ensuring there is some overhang on the sides to help lift the bars out easily after baking.
Make the Shortbread Crust: In a large bowl, combine 2 1/2 cups (300g) of the all-purpose flour, powdered sugar, and salt. Pour in the melted butter and gently mix until the dough forms and comes together evenly. You can also use a stand mixer with a paddle attachment for this step. If desired, add a splash of vanilla extract with the butter for extra flavor.
Bake the Crust: Press the dough evenly into the prepared baking dish, flattening it out with your fingers or the back of a spoon to form a smooth, uniform layer. Bake in the preheated oven for approximately 20 minutes, or until the crust turns a delicate golden color.
Prepare Lemon-Sugar Mixture: While the crust bakes, place the granulated sugar in a food processor and add the lemon zest. Pulse until the zest is fully integrated into the sugar and the mixture appears pale yellow. If you don’t have a food processor, finely mince the zest and mix thoroughly with the sugar by hand.
Mix the Filling: In a large bowl, combine the lemon-sugar mixture with the remaining 1/2 cup (60g) of flour. Add the freshly squeezed lemon juice and crack in the eggs. Whisk everything together vigorously until the filling is smooth and well combined.
Bake the Lemon Filling: Pour the lemon filling evenly over the warm, baked crust. Return the pan to the oven and bake for about 25 minutes. For even cooking, rotate the pan halfway through the baking time. The filling should be set but slightly jiggly in the center.
Cool and Chill: Remove the lemon bars from the oven and allow them to cool at room temperature for about one hour. Then transfer the pan to the refrigerator and chill for at least two hours to let the filling fully set.
Serve: Once chilled, dust the top with powdered sugar. Use a clean, sharp knife dipped in warm water to cut the bars into squares, wiping the knife clean between cuts for neat edges.