Make the cookies: In the bowl of an electric mixer fitted with the paddle attachment, cream butter and granulated sugar until completely smooth, about 3 minutes. Add egg, and continue mixing until well combined. In a small bowl, whisk together cocoa powder and flour. Add dry ingredients to butter mixture, and continue mixing, scraping the sides of the bowl down, until just combined. Divide the dough in half, and shape each half into a small disk; wrap in plastic wrap. Refrigerate until firm, at least 1 hour. (The dough can also be made a day ahead and refrigerated overnight.)
Preheat oven to 350 degrees F.
Line 2 baking sheets with silpat nonstick baking mats or parchment paper. Lightly sprinkle a clean work surface with confectioners' sugar. Place the chilled dough on the work surface. Roll out dough to 1/8-inch thick. (Save the scraps to refrigerate and roll out again.) Using a 2-inch cookie cutter, cut out the cookies, and place on the prepared baking sheets, about 1/2-inch apart. You should be able to fit about 35 cookies on a baking sheet. Bake until you can smell the chocolate, about 12 minutes. Remove to a rack to cool.
Meanwhile, make the ganache: In a small saucepan, bring cream to a boil over medium-high heat. Very finely chop 6 ounces of chocolate, and add to hot cream. Stir with a rubber spatula until the chocolate is melted and smooth. Add peppermint oil. Let cool slightly, about 10 to 15 minutes.
Transfer ganache to a pastry bag fitted with a #11 tip. Pipe out quarter-size amounts of chocolate, about 1 teaspoon each, onto the center of half the cooled wafers. Top with the remaining wafers. Chill in the refrigerator until firm, about 10 minutes.
Melt remaining chocolate in the top of a double boiler over medium heat. Let cool slightly. Dip 1 side of the cookie sandwich to coat. Remove excess chocolate by scraping the cookie against the side of the bowl. Return to the refrigerator until chocolate is set, about 10 minutes.
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