Combine first 2 ingredients in heavy large saucepan. Stir over low heat until chocolate melts and mixture is smooth. Remove pan from heat. Mix in finely crushed mints and 6 1/2 tablespoons sugar. Cool mixture to lukewarm, stirring occasionally, about 30 minutes. Whisk eggs into chocolate mixture, 1 at a time, then whisk in vanilla extract and peppermint extract. Whisk flour, baking powder, and salt in small bowl to blend. Whisk flour mixture, then chopped chocolate into chocolate mixture. Cover batter and chill until firm enough to shape, at least 3 hours and up to 1 day.
Position rack in center of oven and preheat to 325°F. Line 2 baking sheets with parchment paper. Using 1 generous tablespoonful for each cookie, roll dough between moistened palms into 1 1/4-inch-diameter balls, then arrange on prepared baking sheets, spacing 1 inch apart. Bake cookies, 1 sheet at a time, until puffed and cracked on top but still soft to touch in center, about 11 minutes. Let stand on sheets 5 minutes. Press coarsely crushed mints onto tops of cookies or sprinkle with powdered sugar. Transfer to racks; cool completely. (Can be made 1 week ahead. Store airtight between sheets of waxed paper in refrigerator.)
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