Preheat the oven to 325 and prepare an 8x8 pan with parchment paper. Set to the side.
In a medium-sized bowl, make the crust. Combine the melted butter, sugar, vanilla, and salt in a bowl. Mix until combined and then add in the flour. Mix until everything is smooth. The mixture may not fully come together and that is okay.
Take the dough and place it in the prepared pan. Use your hand or a rubber spatula to flatten the dough in the pan until flat. Place the pan in the oven and bake the crust for 20-22 minutes, until golden brown. When done, take the crust out of the oven and use a fork to poke holes in the crust. Set to the side.
Make the lemon filling. Sift the sugar and flour into a medium-sized bowl. Then, add the eggs and whisk until combined. Add in the lemon juice and zest and mix to combine.
Pour the filling over the prepared crust and place the pan back in the oven. Bake the bars for 22-26 minutes, until the filling is set and not jiggling in the pan.
Let the bars cool outside of the oven for 30 minutes, and then place the bars in the refrigerator to chill for 2 hours. After chilling, top with powdered sugar if desired, and cut to serve.
