Add the cold heavy whipping cream, sugar, and vanilla extract to a large mixing bowl or the bowl of a stand mixer.
Begin beating the mixture at medium speed until it starts to thicken slightly, then increase to medium-high speed to continue whipping.
Watch closely as the texture changes and stop once your desired consistency is reached. For a softer texture, the cream should form gentle peaks that curl slightly when lifted. For a firmer texture, continue beating until the peaks hold their shape firmly.
Serve immediately for the best texture, or cover and refrigerate if using later.