Pour the cold cream into the bowl of a food processor. Sift in the powdered sugar and add the vanilla.
With the whisk attachment fitted, turn the mixer on medium-low speed until it starts to thicken, then gradually turn it up to high speed.
Whip until you see thick grooves forming in the cream from the whisk. Check frequently until it reaches the desired thickness - stiff peaks for piping or slightly softer for topping desserts with.
Make sure you don't overwhip the cream - I like to get it close to stiff peaks and then finish it off with a hand whisk.
Notes
It's very important that you use a cream with a high fat percentage - at least 35%. That's why it needs to be heavy cream or heavy whipping cream (double cream in the UK). If you use a cream with a lower fat percentage (such as half-and-half) then it won't whip up properly and won't hold its shape. *For a less sweet version, you can just leave out some of the powdered sugar according to preference.