In a large 8-quart punch bowl, combine vodka, coffee liqueur, peppermint schnapps, and heavy cream. Stir gently to blend. Top the punch with a generous layer of whipped cream. Sprinkle crushed candy canes over the whipped cream for a festive touch. Serve with a ladle, pouring into glasses. Garnish each glass with a dollop of whipped cream, a sprinkle of crushed candy cane, and a peppermint stick for stirring.