Cream butter and sugar with a mixer till fluffy. Beat in salt, egg, peppermint extract, and green food coloring till well blended. Stir in flour.

Divide the dough in thirds and roll each section into a log about 1" wide. Roll each log in green sugar, then wrap in plastic wrap. Chill for at least 2 hours or up to a week.

When you are ready to bake the cookies, preheat the oven to 350 degrees.

Unwrap one of the logs and cut it into slices about 1/4 inch thick. To assemble cookies, place three circles on a lightly greased baking sheet. 

To make stems, cut one circle into three strips. Place a stem at the bottom of the cookie, pressing it up in between the clover petals. Then use your fingernail to press in the sides of the circles to make a clover shape.

Repeat with the remaining dough.

Bake at 350° for 7-8 minutes. Let them sit on the cookie sheet for about 5 minutes, then carefully place them on cooling racks to cool completely.