In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl with an electric hand mixer, beat butter until soft shiny and light in color.
Add sugar and beat until combined.
Add eggs, lemon extract and lemon zest.
Sift together cream of tartar, baking soda, fine sea salt and flour.
In 3 batches, add dry ingredients to wet ingredients.
Turn into a piece of plastic wrap and chill for 1 hour, but up to 24 hours. Using plastic wrap ensures the dough won't dry out.
Preheat oven to 375 degrees and line an insulated baking sheet with parchment paper.
Roll dough into 1 1/2 inch balls and then dip and roll in sugar (and lemon zest, if desired).
Place 2 inches apart on baking sheet.
Bake for 10 minutes, or until just cracking. You should be able to see shiny dough inside the cracks, which means the cookies are done.
Allow to cool for 2-3 minutes on the cookie sheet and then carefully transfer to a cooling rack.
If you've tried this recipe, come back and let us know how it was!
Notes
If you use salted butter, omit the additional fine sea salt.