In the bowl of an electric stand mixer, using the paddle attachment whip butter on medium high speed until nearly white and very fluffy, about 7 - 8 minutes, frequently scrapping down the sides and bottom of the bowl (note that if you have the paddle attachment that constantly scrapes the bowl you can reduce the time by several minutes). Blend in vanilla extract. Add in powdered sugar and heavy cream and mix on low speed until combined, then increase speed to medium and beat until very light and fluffy, about 5 - 6 minutes, frequently scraping down the sides and bottom of the bowl. Spread over cooled cupcakes.
The butter should be soft - not cold and not melted so if doing it in the microwave be sure to do it in low increments (like 4 seconds) and rotate butter between increments just until soft.