Preheat oven to 350°F
Crust
1 cup butter, room temperature
1/2 cup powdered sugar
1 teaspoon vanilla
2 cups flour
Filling
4 eggs, room temperature
2 cups sugar
Grated lemon rind from 2 lemons (3 if using Meyer lemons)
1/2 cup lemon juice
Prepare crust and bake in 350°F for 20 minutes.
Grease a 9x13 pyrex pan with butter. Cream the butter and add the powdered sugar and vanilla. Add in the flour and mix well. Spread evenly on the bottom and about an inch up the sides of pan. You don't want the filling to breach the edges of the crust or you will end up with a dark, sticky mess. I use the palm of my hand to flatten the crust out. It always seems like there isn't enough dough, but be patient and work it in. Using a pyrex pan allows you to hold the pan up to the light to see thinner (brighter) portions of the crust. Avoid any thin spots to prevent burning.
Bake the crust in a 350°F oven for 20 minutes or until very lightly browned on the edges. You are going to cook this with the filling for another 20 minutes, so less brown is better here.
Prepare the filling. Pour into hot, baked crust and bake for 20 minutes.
Separate yolks from eggs and beat egg yolks in mixer (you can freeze the whites or use in another recipe). Use a microplane grater to get only the very outer rind of the lemons before juicing them. Add the lemon rind, juice and sugar to eggs, being careful not to whip too much air into it. Make sure you mix long enough to fully dissolve the sugar granules. Room temperature eggs will help dissolve the sugar faster. Pour the filling into hot, finished crust (right when it comes out of the oven). Carefully return to crust and filling to oven and bake another 20 minutes (worry more about spilling/breaching sides of crust than losing oven heat).
Let cool and dust with powdered sugar prior to serving.
These are best served with a light dusting of powdered sugar. The easiest way to do this is just sift the powdered sugar right over the lemon bars. The finished lemon bars will leach moisture into the powdered sugar topping, making for an unattractive treat in only a few hours. It is best to dust each serving right before plating.
Cover the pan with foil or lid to keep bars fresh. They should keep for 2-3 days at room temperature or longer in the refrigerator, but it is rare to have any left after 2 days.