Beat powdered sugar, butter and egg in large bowl with electric mixer on medium speed, or mix with spoon. Stir in flour and salt. Divide dough in half. Stir cocoa and milk into one half; stir chocolate shot, wintergreen extract and food color into other half.
Roll or pat chocolate dough into 12x6 1/2-inch rectangle on waxed paper. Shape peppermint dough into 12-inch long roll; place on chocolate dough. Wrap chocolate dough around peppermint dough, using waxed paper to help lift. Press edges together. Wrap and refrigerate about 2 hours or until firm.
Heat oven to 375°F. Cut roll into 1/4-inch slices. Place about 1 inch apart on ungreased cookie sheet. Bake 8 to 10 minutes or until set. Remove from cookie sheet to wire rack; cool.