In the bowl of an electric mixer, cream together butter and brown sugar until smooth and fluffy, scraping the bowl as needed. Add the eggs, lemon zest, and lemon juice and beat until smooth. 

Sprinkle the salt, rosemary, and flour on top. Beat on low speed until the dough comes together and no streaks of flour remain. 

Pat the dough into a ball and set it on a piece of saran wrap. Wrap the dough up then pat it down into a rough rectangle about a 1/2 inch thick with your hands. Refrigerate for at least 2 hours or up to 48 hours. 

When ready to bake, preheat the oven to 350 degrees. Line 2 baking sheets with parchment paper. Place the coarse sugar in a bowl.

Lightly flour your counter top then place the dough on top. Flour a rolling pin, then roll your dough out to about 1/4 inch thick. Using a cookie cutter or small juice glass, cut circles of dough out. Roll the edges of the dough in the coarse sugar then line up on the parchment paper, spacing at least 1 inch apart. Re-roll and cut the dough until none remains. Bake for 8-10 minutes or until edges are very light golden brown and centers look set.