Preheat the oven to 325°F. Line the bottom of an 8x8 baking dish or small oven safe vessel depending upon the portions you are making with parchment paper (use foil if needed), leaving an overhang on the sides to lift the finished bars out. Set aside.
For the crust: Mix the melted butter, powdered sugar, vanilla extract, and a pinch of salt together in a bowl. Add the flour and stir to completely combine. The dough will be crumbly. Press it firmly into the bottom of the prepared baking dish, making sure the layer of crust is nice and even. Bake for 10 minutes, then remove from the oven. Set aside.
For the filling: Whisk the eggs, granulated sugar, lemon juice, and lemon zest until completely combined. Then whisk in the flour until smooth.
Pour filling over warm crust. Bake the bars for about 15 to 18 minutes or until the center is relatively set and no longer jiggles (give the vessel a light tap with an oven mitt to test). Remove bars from the baking dish and cool at room temperature, trim off a sliver of the sides if desired for presentation, then refrigerate until chilled, about 1 to 2 hours.
Dust the top with powdered sugar and portion into 6 or 9 squares as you prefer before serving.