Lightly butter a 9 by 13-inch baking dish with 2 teaspoons of the butter and line with 1 sheet of parchment or waxed paper. Butter the top of this sheet of paper with 1 teaspoon of the remaining butter and then lay a second sheet of parchment or waxed paper crosswise over the first sheet. The parchment should be cut large enough so that the sides are even with the top of the baking dish; this extra paper will function as handles to help you remove the lemon squares from the pan later. Set pan aside.
In a large bowl combine 1 3/4 cups of the flour, 2/3 cup of the confectioners' sugar, the cornstarch, and 3/4 teaspoon of the salt and mix thoroughly. Cut the remaining 12 tablespoons of butter into small pieces and add to the flour mixture. Using your hands, 2 forks, or a pastry blender, work the butter into the flour mixture until the mixture resembles coarse meal. Transfer the butter-flour mixture to the prepared baking dish and press into an even 1/4-inch layer along the bottom and partly up the sides of the pan. Refrigerate for 30 minutes.
While the crust is chilling, preheat the oven to 350 degrees F.
Bake the crust until golden brown, about 20 to 25 minutes.
While the crust is baking, assemble the filling by combining the eggs, granulated sugar, flour, and lemon zest in a medium bowl and whisking until smooth. Stir in lemon juice, milk, limoncello, and remaining pinch of salt and mix well.
When the crust is golden brown, remove it from the oven and reduce the oven temperature to 325 degrees F. Stir the lemon mixture again, then pour onto the warm crust. Bake until the filling is set, about 20 minutes. Transfer to a wire rack to cool completely. Grasp the waxed paper that lines the 2 longest sides of the baking dish and remove the bars from the pan by pulling up gently. The entire dessert should easily dislodge and come away from the pan. Transfer to a cutting board and, using a clean knife, cut into squares, wiping knife after each cut. Place a small amount of confectioners' sugar into a small sieve, and sprinkle the bars with the sugar. Serve immediately, or refrigerate, wrapped with plastic wrap, up to 2 days, until ready to serve.
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