Beat butter or margarine in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking soda, gingerroot, nutmeg, and cloves; beat until combined, scraping sides of bowl occasionally. Beat in molasses and egg until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon.
Drop dough a scant 1/4 cup at a time 4 inches apart onto an ungreased cookie sheet. Bake in 350 degree F oven for 12 to 14 minutes or until edges are firm. Transfer cookies to wire racks and cool. Spoon Lemon Icing over warm cookies to glaze tops. Makes 12 cookies.
Combine powdered sugar, butter or margarine and lemon peel in a small mixing bowl. Stir in lemon juice. Stir in milk till icing is smooth and of drizzling consistency.