Preheat the oven to 350 degrees.
Line a 9x13 inch pan with parchment paper.
Begin making the shortbread crust by adding the butter and sugar to the bowl of an electric mixer fitted with the paddle attachment. Beat until light, fluffy, and thoroughly combined.
Add the vanilla and beat until combined.
Add the flour and beat until combined. Be sure to scrape the bottom and sides of the mixer bowl.
Press the dough down in a single layer along the bottom of the parchment paper lined baking pan. You should work out the dough from the middle to the edges, being sure to get a fairly even layer - especially in the corners.
Prick all over the surface of the dough to prevent it from puffing up in the oven.
Bake about 18 minutes. The dough should be barely golden.
While the dough is baking, prepare the rest of the layers.
Zest two lemons.
Squeeze 1/2 cup of lemon juice, about 3-4 lemons.
Combine the sweetened condensed milk and the lemon juice and lemon zest in a small mixing bowl. Set aside.
Separate the egg whites and egg yolks. You can keep the yolks for a different recipe or discard.
Add the four egg whites in the bowl of a stand mixer fitted with the whisk attachment.
Add the cream of tartar to the egg whites.
Beat on medium speed until soft peaks form.
Increase the speed to medium high and slowly add in the sugar. I usually add in about a tablespoon at a time.
Continue beating until stiff peaks form. You know you have reached this stage when you turn the whisk attachment upside down and the egg white peak doesn't move. Likewise, the eggs won't slip out of the the bowl.
Spread the lemon mixture in an even layer over the baked shortbread crust.
Spread the meringue layer on top of the lemon layer. Be careful not to press down too hard as you don't want them to mix.
I like to make a swirly peak pattern with the meringue. You can do that with an offset spatula or with a spoon.
Return to the oven and bake until the meringue is golden brown, another 15-20 minutes.
Let cool completely before removing from the pan and slicing.