Preheat the oven to 325°F. Line a 13 x 9-inch baking dish with parchment paper, leaving an overhang on two opposite sides to use as a sling.
In a medium mixing bowl, stir together the sugar, salt and vanilla extract. Stir in the flour and melted butter until a crumbly dough forms.
Press the dough evenly into the bottom of the prepared baking pan, crust will be thin. Generously prick with a fork and then refrigerate for 30-45 minutes.
Bake for 15-20 minutes or until crust is starting to brown. Remove and allow to cool while you make the filling.
Lemon Filling
Increase the oven temperature to 350°F.
In a large bowl, or the bowl of a stand mixer fitted with the paddle attachment, combine the sugar, flour, lemon zest, salt and vanilla. Whisk in the eggs, lemon juice and milk until fully blended.
Pour the lemon mixture over the crust.
Bake until the lemon filling is set in the center and it no longer wiggles when the pan is moved, about 30-35 minutes. Remove before the lemon bars are lightly browned.
Remove and cool on a wire rack until room temperature and then chill for 1-2 hours.
Carefully remove the bars using the parchment sling. Place onto a cutting board and slice into 16 bars, cleaning the knife between each slice.
Right before serving, dust with powdered sugar.
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