Chill deep bowl and beaters of electric mixer in freezer for at least 20 minutes.
(If freezer is too crowded to fit bowl, place beaters in bowl, fill bowl with ice water, and chill on counter. When bowl and beaters are well chilled, dump out water and dry thoroughly.) Add cream, sugar, and vanilla to chilled bowl.
Beat on low speed until small bubbles form, about 30 seconds.
Increase speed to medium and continue beating until beaters leave a trail, about 30 seconds.
Increase speed to high and continue beating until cream is smooth, thick, and nearly doubled in volume, about 20 seconds for soft peaks or about 30 seconds for stiff peaks.
If necessary, finish beating with whisk to adjust consistency.
Serve immediately or spoon into fine sieve or strainer set over measuring cup and refrigerate for up to 8 hours.