Preheat the oven to 350°F and line an 8 x 8 pan with parchment paper on all sides. Set aside.
In a standing mixer with the paddle attachment, on medium speed beat together the butter, sugar, flour, and salt until the mixture comes together. The mixture will be crumbly. Make sure not to over mix.
Press the dough in an even layer into the prepared pan. Use a fork to make a few holes in the crust. Blind bake the crust for 20 minutes.
While the crust bakes, make the lemon layer. Sift the sugar and flour together in a large bowl to get rid of any clumps. Add the eggs, lemon juice, and lemon zest and whisk well until completely combined. The mixture will be thin.
Take the crust out of the oven and pour the lemon layer over the blind baked shortbread crust.
Lower the oven temperature to 325°F and bake for 20-25 minutes or until the center no longer jiggles. Take the bars out of the oven and allow to cool completely.
Once the bars are completely cool, transfer to the fridge to set for 2 hours (or overnight). Slice the lemon bars and serve cold with a dusting of powdered sugar.