Using a clean bowl, beat the heavy cream on high speed until stiff peaks form. Place bowl in the refrigerator to chill.
In a separate bowl, beat the cream cheese, powdered sugar and vanilla extract until smooth and well combined.
Fold ⅓ of the whipped cream into the frosting and gently stir until well combined. Fold the remaining whipped cream into the cream cheese mixture; gently stir until well combined.
A reader noted in the comments that she uses whipped topping (i.e. Cool Whip) to make this cake, and it has always worked well. I haven't personally tried that yet, but I can totally see how it would work as whipped topping is more stable than whipped cream. If you give this one a shot with whipped topping, let me know how it turns out!