3 cups frozen whipped topping (such as Cool Whip®), thawed
Beat the whipping cream, instant pudding mix, milk, and vanilla extract together with an electric hand mixer in a large bowl until soft peaks start to form. Lift your beater or whisk straight up: the mixture will form soft mounds rather than a sharp peak.
Fold the whipped topping into the whipping cream mixture to evenly mix. Refrigerate until ready to use.