In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl with an electric hand mixer, beat the butter until soft shiny and light in color.
Add the sugar and beat until combined.
Add the eggs, lemon extract and lemon zest.
Sift together the cream of tartar, baking soda, fine sea salt and flour.
In 3 batches, add the 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 the oven to 375°F and line an insulated baking sheet with parchment paper.
Roll the dough into 1 1/2 inch balls and then dip and roll in granulated sugar (and lemon zest, if desired).
Place the cookies 2 inches apart on the 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. They may look undercooked, that is normal!
Allow the cookies to cool for 2-3 minutes on the cookie sheet and then carefully transfer to a cooling rack.
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Notes
If you use salted butter, omit the additional fine sea salt.