In a large bowl, whisk the eggs, egg yolks, granulated sugar, salt, cream of tartar, and vanilla extract.
In a medium bowl, whisk the fresh-squeezed lemon juice and flour until smooth and the flour is dissolved.
Melt the butter in a large pot. Add the flour and lemon juice mixture and cook over medium heat, whisking constantly until thickened.
Carefully pour the hot lemon mixture into the bowl with the eggs, whisking the egg mixture constantly so the eggs don't scramble. Add everything back into the pot and return to the stove over medium heat. Bring the mixture to a boil, whisking constantly until thick. You'll want to cook it for about 6-8 minutes over medium heat and keep whisking the entire time. Once the mixture comes to a boil it will thicken rapidly.
Remove from heat and strain the mixture through a sieve into a large bowl. Use a whisk to promote it going through the sieve. Use a spoon to scrape the strained curd from the opposite side of the sieve. Once you have most of it strained through, use a spoon to push as much of it as you can through the sieve.
Pour the strained lemon curd into the warm prebaked crust and use a spatula to spread it out evenly. Bake for 12-14 minutes. Remove from the oven and let cool to room temperature. Cover the pan and refrigerate for at least 3 hours (overnight is best) before slicing and serving. Dust the tops of the lemon bars generously with powdered sugar before serving.