Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in cocoa until well blended. Press into ungreased 13x9-inch pan. Bake 10 to 12 minutes or just until set. Cool completely.
Crumble baked cookie. Gently press half of the cookie crumbs into bottom of ungreased 8-inch springform pan. Spread softened vanilla ice cream over cookie mixture in pan. Evenly top with remaining crumbled cookies; press gently to make an even layer. Top with peanut butter ice cream. Cover pan with foil; freeze 8 hours.
Remove side of pan. Place ice cream cake on serving plate. Frost top and side with whipped topping. Sprinkle with chocolate-covered peanuts. Store covered in freezer.