Preheat the oven to 350℉. Lightly grease an 8x8 pan and line it with parchment paper. In a bowl, mix together the flour, powdered sugar, and salt. With your hands, rub the butter into the flour until combined and there are little to no butter streaks.

Pour the shortbread into the lined 8x8, spreading it evenly. Briefly freeze the shortbread for 5 minutes, to firm it up.

Dock the shortbread dough all over with a fork, then bake for around 25-30 minutes, until set and lightly browned.

Adjust the oven temperature to 325℉. In the meantime, make the filling. In a medium saucepan, rub together the sugar and lemon zest with your fingers for 1-2 minutes, until it is fragrant and begins to clump slightly. Whisk in the salt, eggs, and egg yolks, until the mixture lightens in color.

Stream the lemon juice into the egg and sugar mixture, whisking constantly, until it is fully combined and slightly thickened. Place the saucepan on medium heat and whisk constantly, until the mixture is opaque, covers the back of a spoon, and reaches 170℉. Do not overcook.

Take the saucepan off of the heat and add the butter, stirring until melted and well incorporated. Hold a sieve over the prepared crust and pour over the lemon curd. Discard any lumps in the sieve, then smooth the surface of the curd.

Bake the lemon bars for 20-30 minutes at 325℉, until the filling puffs and has a slight wobble in the center. Let the lemon bars cool, uncovered, in the fridge (preferably overnight). Once completely cool and firm, lift the bars out of the pan and slice into 16. Right before serving, dust the bars with powdered sugar. Dust with more powdered sugar or serve with whipped cream, if desired, to cut the tartness.