Sift together flour, cocoa, baking soda and salt into medium-size bowl; set aside. In large bowl, beat together sugar and butter until smooth and creamy. Beat in egg, then vanilla and mint extract.
On low speed, beat flour mixture into butter mixture. Divide dough in half; shape each into a log about 1-1/2 inches in diameter. Wrap in plastic wrap; refrigerate 3 to 4 hours.
Heat oven to 375 degrees °F. Cut each log into slices, 3/16 inch thick; place on ungreased baking sheet.
Bake in 375 degree F oven for 8 to 10 minutes or until almost firm. Transfer cookies to wire rack to cool.
Beat together powdered sugar, butter, milk and mint extract in medium-size bowl until good spreading consistency. Divide filling in half; tint half with red food coloring, and other half with green food coloring.
Spread flat side of one-quarter of the cookies with red filling and one-quarter with green filling. Top each with a plain cookie. Chill until set.
