Line a square baking dish with parchment paper, cutting it to fit the bottom and two longer sides. Brush the parchment with a little melted butter to help it stick.
For the shortbread crust: In a bowl, combine 1¼ cups all-purpose flour, 5 tablespoons powdered sugar, and ½ teaspoon kosher salt.
Add 10 tablespoons of cold unsalted butter, cut into cubes, to the flour mixture.
Using your fingertips, smash the butter into the flour mixture until it forms a crumbly, shaggy dough with a uniform texture, similar to pie dough but more blended.
Perform the 'fraisage' technique: Bring the dough together, then use a bowl scraper to smear the dough little by little across the board to further blend the butter into the flour mixture, creating a more uniform texture.
Scrape the dough into the bottom of the prepared baking dish.
Pat the dough evenly into the bottom of the pan with your fingertips. If the mixture becomes sticky, chill it in the fridge for 5-10 minutes.
Prick the shortbread dough with a fork in about 8-10 spots to help steam escape.
Chill the crust in the freezer for about 5 minutes.
Bake the crust in a preheated oven at 350°F (175°C) for 25-30 minutes, or until golden brown.
While the crust bakes, prepare the lemon curd filling: In a saucepan, combine 1½ cups granulated sugar and 2 tablespoons of finely grated lemon zest. Massage the zest and sugar together to release the zest's oils.
Add a pinch of kosher salt and 3 large eggs and 9 large egg yolks to the saucepan.
Whisk the egg and sugar mixture thoroughly until it becomes several shades paler and lighter in texture (this is called blanching).
Slowly stream in 1½ cups of strained lemon juice, whisking to incorporate and thin out the mixture.
Cook the curd mixture over medium heat, whisking constantly, until it thickens and coats the back of a spoon, forming opaque lines when a finger is run through it. Lower the oven temperature to 325°F (160°C) while the curd cooks.
Remove the saucepan from the heat and whisk in 1 stick of butter, one piece at a time, until fully incorporated.
Strain the lemon curd over the baked crust to remove any solids.
Smooth the surface of the lemon curd filling.
Bake the lemon bars at 325°F (160°C) for 25-30 minutes, or until the filling is set with a slight wobble and bubbling around the edges.
Let the lemon bars cool completely, then cover and chill in the refrigerator overnight.
Once fully chilled, unmold the lemon bars by lifting the slab out of the baking dish.
Cut the lemon bars into desired sizes, cleaning the knife with a wet paper towel between cuts for sharp edges.
Dust the top of the lemon bars generously with powdered sugar just before serving.
