Preheat your oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, allowing overhang on the sides to create handles for easy removal later.
In a stand mixer fitted with the paddle attachment, cream together the butter and sugar until light and fluffy, approximately 3-4 minutes.
Add flour and salt to the butter mixture, mixing on low speed until just combined. The mixture will look crumbly but should hold together when pressed between your fingers.
Press the dough evenly into your prepared pan, creating a flat, compact layer. For the most even crust, use the bottom of a measuring cup to compress the dough.
Bake the crust for 15-20 minutes until the edges are just beginning to turn golden.
While the crust bakes, whisk together eggs and sugar until well blended. Add the lemon juice and whisk until smooth. Fold in the flour and lemon zest, stirring carefully to avoid incorporating air bubbles.
Pour the filling over the hot pre-baked crust immediately after removing it from the oven. Return to the oven and bake for 25-30 minutes until the filling is set and no longer jiggles in the center.
Allow the bars to cool completely at room temperature, then refrigerate for at least 2 hours before cutting.
Use the parchment paper handles to lift the entire dessert from the pan. With a sharp knife dipped in hot water and wiped clean between cuts, slice into 24 bars. Dust with powdered sugar just before serving.