Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in cocoa until well blended. Press in bottom of ungreased 8-inch square pan.
Bake 20 to 24 minutes or until set. Immediately sprinkle with milk chocolate chips. Cover with foil; let stand 5 minutes to melt. Spread melted chocolate evenly. Refrigerate about 45 minutes or just until chocolate is set.
In small microwavable bowl, microwave white vanilla baking chips uncovered on High about 1 minute, stirring frequently, until melted and smooth. Stir in peppermint extract. Spread over milk chocolate layer. Place candies in food-storage plastic bag. Seal bag; coarsely crush with rolling pin or meat mallet. Sprinkle crushed candies on top. Refrigerate about 45 minutes or just until set. For squares, cut into 4 rows by 4 rows.