Preheat the oven to 350°F (175°C) and prepare a 9x13-inch baking dish by lining it with parchment paper. Combine 2 1/2 cups of the flour with the powdered sugar and salt in a bowl, then stir in the melted butter until the mixture is fully incorporated; a stand mixer with paddle attachment may also be used. If desired, a splash of vanilla can be mixed in with the butter at this stage. Scatter the dough evenly into the lined pan and press firmly into a flat layer. Bake for about 20 minutes or until the crust takes on a pale golden hue. Meanwhile, place the granulated sugar and lemon zest in a food processor and pulse until the zest is thoroughly blended into the sugar, creating a fragrant, pale yellow mixture; alternatively, finely mince the zest and stir into the sugar by hand. Transfer the zested sugar to a large bowl, add the remaining 1/2 cup of flour, and mix to combine. Pour in the fresh lemon juice and crack in the eggs, whisking diligently until the filling is completely smooth and uniform. Once the crust is ready, pour the lemon mixture over the warm base and return to the oven, baking for approximately 25 minutes while rotating the pan halfway through. Remove from the oven and allow to cool at room temperature for one hour before chilling in the refrigerator for an additional two hours. Once set, dust generously with powdered sugar and slice into bars using a clean, sharp knife, wiping the blade after each cut for neat edges.