Preheat your oven to 350 degrees Fahrenheit and line a 9×13 inch baking pan with parchment paper.
In a stand mixer, cream the butter and 1/2 cup of sugar until the mixture is light and fluffy.
Add the flour and salt to the mixer, blending on low speed until the dough reaches a sandy consistency.
Press the shortbread crust mixture firmly into the bottom of the prepared 9×13 pan, ensuring an even surface.
Bake for 15 to 20 minutes until the edges are a light golden brown.
While the crust bakes, whisk together the eggs, the remaining 2 cups of sugar, fresh lemon juice, and lemon zest in a large bowl until fully combined.
Pour the lemon filling over the warm crust immediately after removing it from the oven.
Reduce the oven temperature to 325 degrees Fahrenheit and bake for another 20 to 25 minutes until the filling is just set.
Remove from the oven, let the bars cool completely, and chill in the refrigerator before dusting with powdered sugar and portioning into 20 bars.