In a large mixing bowl, beat butter with an electric mixer on medium speed for 30 seconds. Add granulated sugar, brown sugar, cocoa powder, baking powder and baking soda. Beat until combined, scraping sides of bowl occasionally. Add eggs and vanilla to sugar mixture; beat until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon. Cover and chill dough for 2 to 24 hours, or until easy to handle.

Roll dough into 1-1/2-inch balls and place 3 inches apart on ungreased cookie sheets (or, for smaller cookies, roll into 3/4-inch balls and place 2 inches apart). Bake in a 375 degree F. oven for 8 to 10 minutes (or 6 to 7 minutes for smaller cookies) or until edges are set. Let stand 1 minute on cookie sheet. Transfer cookies to wire racks and let cool.

Frost the tops of half of the cookies with Chocolate Glaze. Place cookies, chocolate sides up, on a wire rack. Let stand until set (about 30 minutes).

Spread the bottoms of the remaining plain cookies generously with the Creme de Menthe Filling. Top with chocolate-coated cookies, chocolate sides up. Gently press the cookie to spread the filling into an even layer. Wrap each cookie in plastic wrap and chill in the refrigerator for at least 2 hours. Serve cold. (Store any leftover cookies in the refrigerator up to 4 days or freeze up to 1 month.) 18 large or 36 small cookie sandwiches.

In a small saucepan, cook and stir 1/3 cup whipping cream and 6 ounces finely chopped bittersweet or semisweet chocolate over low heat until chocolate melts. Remove from heat. Let cool about 20 minutes or until it slightly thickens. (Chocolate should be warm but not hot.) Makes about 3/4 cup.

In a large mixing bowl, combine 1/3 cup butter, softened, and 3 tablespoons green creme de menthe or creme de menthe syrup. Gradually add 4 cups powdered sugar, beating with an electric mixer on medium speed until smooth. If necessary, add 1 tablespoon additional green creme de menthe or syrup to make of spreading consistency. (Or, if you like, substitute milk for green creme de menthe. Add 1 1/2 teaspoons vanilla, 1/2 teaspoon peppermint extract and 2 or 3 drops green food coloring.) Makes about 2 cups.