Preheat oven to 325 degrees. Line the bottom and sides of a 9 x 13 pan with parchment paper. Let it overhang over the sides of the pan to make it easy to remove the bars from the pan.
In a small bowl, stir together butter, sugar, flour, vanilla extract, and salt. Press evenly in the prepared pan. Bake for 18-20 minutes.
While baking, make the lemon filling. In a medium bowl, whisk together eggs, sugar, lemon juice, and flour until completely smooth. Once the crust is parbaked, pour over hot crust and return to the oven.
Bake for 20-22 minutes. Don't overbake the lemon bars. Let cool to room temperature. Chill in the refrigerator. The lemon bars taste best chilled. Sprinkle powdered sugar all over the lemon bars and cut into squares.
*Recipe adapted from Sally's Baking Addiction.