In a medium sized mixing bowl, cream the butter until it is light and fluffy. Add the sugar, rosemary and lemon zest, beating until well blended. Scraping down the sides of the bowl as needed, add the 2 egg yolks. Mix until completely incorporated.
To this mixture add the flour, baking soda, and salt. Mix well. The cookie dough will be stiff. Cover the bowl with plastic wrap and place in the fridge to chill for 30 minutes.
Towards the end of the chilling time, prepare 2 baking sheets with parchment paper or silicone baking pads. Preheat the oven to 350 degrees.
Roll the dough into 1 1/4 inch balls and place at least 2 -2.5 inches apart on the baking sheets. Flatten each ball of dough to about 1/4 inch thick with the bottom of a glass that's been dipped in flour.
Mix the remaining sugar and lemon zest together. Before baking brush each cookie lightly with the egg whites and sprinkle with lemon sugar. Bake at 350 degrees for 12-15 minutes or until the edges of the cookies are golden brown.
Let cool on the baking sheets for 2 minutes before removing to a wire rack to cool completely. Store in an air tight container.