PREPARATION:

1. For cookies, beat butter and sugars in large bowl with electric mixer at medium speed until creamy. Add melted chocolate, egg and vanilla; beat until well blended, scraping down bowl occasionally. Combine flour, cocoa and salt in small bowl. Gradually add flour mixture, beating until well blended. Shape dough into 16-inch-long log. Wrap in plastic wrap; refrigerate about 1 hour or until firm.
2. Preheat oven to 400°F. Lightly grease cookie sheets and line with parchment paper. Cut log into 1/3-inch-thick slices. Place slices on prepared cookie sheets. Bake 10 to 12 minutes or until set. Cool 5 minutes on cookie sheets. Remove to wire racks to cool completely.
3. For filling, combine powdered sugar, butter and salt in large bowl; beat until well blended. Add mint extract and food coloring; beat until well blended and evenly tinted. Add enough milk, 1 tablespoon at a time, to make filling fluffy. Spread or pipe filling on bottoms of half the cooled cookies. Top with remaining cookies.