Place a mixing bowl (preferably metal) in the freezer for 10 to 15 minutes. Getting the bowl cold will keep the ingredients cold while mixing.
Place bowl back on to the stand mixer fitted with a whisk attachment (or use a hand mixer). Add heavy cream, confectioners' sugar and vanilla to the bowl. Turn the mixer on low speed for 10 to 20 seconds for ingredients to combine, then increase the speed to medium high. Whip for about 1 1/2 to 2 minutes or until the whisk is leaving a trail in the whipped cream and medium soft peaks form.
Place a tablespoon of whipped cream between two chocolate wafers. Start stacking the wafers layering each with a tablespoon of whipped cream. After about 12 wafers, spread a little whipped cream on the serving platter, turn the stack on its side and lay it on the platter. Repeat twice more placing each log next to each other. Spread whipped cream over the top and sides of the cake.
Cover the cake loosely with plastic wrap and chill it in the refrigerator for at least 6 hours or ideally overnight. Before serving, garnish with chocolate shavings, slice and serve.
Store icebox cake loosely covered with plastic wrap in the refrigerator for up to 3 days.Freeze icebox cake after it has been chilled. Wrap it in plastic wrap and aluminum foil to prevent freezer burn. Freeze for up to 1 month.