Preheat oven to 350 degrees. Line a 7x10" or 9x13" baking pan, or a baking pan somewhere in between in size (see notes) with parchment paper then set aside.

To the bowl of an electric mixer, or a large glass bowl if using a handheld mixer, add softened butter, sugar and vanilla then beat until smooth. Add flour and salt then beat until combined. Scoop dough into prepared baking dish then spread into an even layer with your hands. Use a fork to poke shallow holes all over the top, all the way to the edges, then bake until the edges are just barely turning golden brown. A 9x13" baking pan will take ~20 minutes while a smaller pan like 7x10" will take ~25 minutes.

Remove crust from oven then let cool for at least 30 minutes.

While the crust is cooling, add lemon zest, lemon juice, and eggs to a large bowl then whisk to combine. Add sugar and flour then whisk for 1 minute. Pour over partially cooled crust then bake until the center is set and no longer jiggly - a 9x13" pan will take ~20 minutes, while a smaller pan like 7x10" can take ~32-35 minutes. The top will have a white, crackly appearance with tiny bubbles - that's normal!

Let Lemon Bars cool COMPLETELY - several hours or overnight - then use the parchment paper to lift bars out of the baking pan. Slice into small squares then dust with powdered sugar and serve. Store covered on the counter or in the refrigerator for 2-3 days.