Add the heavy cream, sugar + vanilla to the chilled bowl of a stand mixer. Heavy whipping cream whips up better, and remains stable for a longer period of time, the colder it is as it whips. 

Start mixing on low speed to thoroughly combine the ingredients, then slowly work your way up to high speed as you see the cream begin to whip and form soft peaks. Pause, as needed, to scrape down the sides with a rubber spatula.

Continue to whip until you are beating the cream on high speed and stiff peaks form.