Preheat oven to 350°F degrees and line a 9-inch square baking pan with parchment paper or greased foil.
With an electric mixer, beat the butter and sugar together until light and creamy, 2-3 minutes on high.
Add flour and salt and mix until the dough comes together.
Press evenly into the prepared sheet pan and bake until it just starts to turn golden brown, 15-20 minutes.
Let cool for about 15 minutes before adding filling.
To make the filling:
Whisk together the eggs, sugar, lemon juice, lemon zest, and flour until smooth.
Pour on top of the cooled crust.
Bake for a few minutes past the point when the center is set (if you jiggle the pan, the center should not move), about 30-35 minutes.
Cool in the pan for 15 minutes, then lift out of the pan with the parchment paper or foil, and transfer to a wire rack to cool completely before serving. You can chill in the fridge to cool it faster.
Dust the top of the bars with powdered sugar, then slice and serve.