In a large mixer bowl beat butter with an electric mixer on medium speed until softened (about 30 seconds). Add sugar and salt and beat until fluffy.Advertisement
Add the egg, peppermint extract or vanilla, and a few drops of green food coloring. Beat mixture well.
With mixer on low speed gradually add flour to butter mixture and beat well.
Divide dough into 3 equal parts. Shape each part into a roll about 1 inch thick and about 8 inches long. Roll each in green colored sugar. Wrap rolls in plastic wrap. Chill in refrigerator for at least 2 hours or up to 1 week.
Unwrap rolls. Slice crosswise so the slices are 1/4 inch thick. To shape each shamrock, place 3 slices of dough with sides touching in a shamrock shape on an ungreased cookie sheet. Cut a stem from a fourth slice and attach to the shamrock (save the rest of this slice for cutting other shamrock stems). Gently push the slices together so each leaflet curves in slightly.
Bake in a 350 degree F oven about 8 minutes or until edges are light brown. With a pancake turner lift the cookies onto a cooling rack to cool. Makes 32 cookies.
Store the baked cookies in a tightly covered container at room temperature up to 3 days. Or, store the baked cookies in a freezer container in the freezer up to 2 weeks.