Finely grate colored portion of lemon peel using bell grater or hand-held grater. Measure 4 teaspoons; set aside.
Preheat oven to 375 degrees. Place flour, baking soda and salt in large bowl; stir to combine.
To separate egg yolk from white, gently tap egg in center against hard surface, such as side of bowl. Holding a shell half in each hand, gently transfer yolk back and forth between the 2 halves. Allow white to drip down the 2 halves into bowl. When all white has dripped into bowl, place yolk in another bowl. Store unused egg whites in airtight container. Refrigerate for about one week.
Beat butter and 1 cup sugar in large bowl with electric mixer at medium speed until light and fluffy, scraping down side of bowl once. Beat in egg yolks, 3 teaspoons lemon peel and rosemary.
Gradually add flour mixture. Beat at low speed until well blended, scraping down side of bowl once.
Combine remaining 1/4 cup sugar and 1 teaspoon lemon peel in small bowl.
Roll tablespoons of dough into 1-inch balls; roll in sugar/lemon zest mixture to coat.
Place balls 2 inches apart on ungreased cookie sheets. Press balls to 1/4-inch thickness using flat bottom of a drinking glass.
Bake 10 to 12 minutes or until edges are golden brown. Remove cookies with spatula to wire racks; cool completely.
Store tightly covered at room temperature or freeze up to 3 months.