Preheat the oven to 350°F and line a 9x13-inch baking dish with parchment paper.
Combine 2 1/2 cups of flour with powdered sugar and salt in a mixing bowl. Stir in the melted butter until a dough forms. If desired, add a splash of vanilla extract to the mixture.
Spread the dough evenly into the prepared pan, pressing it into a smooth layer. Bake for approximately 20 minutes, or until lightly golden.
While the crust is baking, prepare the filling by adding sugar and lemon zest to a food processor. Blend until the sugar turns pale yellow and the zest is well incorporated. Alternatively, mince the zest finely and mix it with sugar manually.
Transfer the sugar mixture to a large bowl. Add the remaining 1/2 cup of flour and mix thoroughly. Pour in the lemon juice and whisk in the eggs, stirring until fully combined.
Once the crust is ready, pour the filling over the warm crust. Return the pan to the oven and bake for about 25 minutes, turning halfway through for even baking.
Allow the bars to cool at room temperature for 1 hour, then refrigerate for 2 hours to set completely.
Before serving, dust the top with powdered sugar. Slice into bars using a sharp knife, cleaning and dampening the blade between cuts for neat edges.