Rosemary Shortbread Cookies

Cookies:
2 sticks unsalted butter, room temperature
1 tsp fresh rosemary 
½ cup sugar
2 cups all-purpose flour
Optional Herbs: lavender, thyme, basil 

Icing:
2 1/4 cups confectioners' sugar, sifted
2 tablespoons light corn syrup
1 tsp lime juice and ½ tsp lime zest or 1/8 tsp lime oil
1 1/2 to 2 tablespoons plus 1 teaspoon milk

 Preheat the oven to 300 degrees.

1. Combine the rosemary and sugar in a  food processor turn on for 30 seconds to allow the herb oils to flavor the sugar.
2. Beat the butter and sugar together with a paddle in the bowl of an electric mixer until smooth but not fluffy.
3. Add the flour all at once and mix on low speed until the flour is incorporated and begins to form the dough.
4. Roll the dough out on a floured board into two 8-inch logs that are 1 ½ round.
5. Wrap the logs in plastic and chill for at least 30 minutes...wrapped dough can be frozen for up to 3 months if desired.
6. Cut the logs into ¼-inch slices and place on an ungreased cookie sheet.
7. Bake the cookies for 22 to 25 minutes.  Do not let the cookies brown or they will be over baked.
8. Allow the shortbread to cool on the pan for 5 minutes.  Remove to a cookie rack and cool completely before icing.
9. While the cookies are cooling make the icing.  Combine the icing ingredients in a bowl and stir until smooth.  Drizzle the icing in streaks over the cooled cookies (I use a fork).  If the icing is too thick add more milk 1 tsp at a time.  Be careful not to make the icing too runny.  Allow the icing to harden before serving and storing for later use.