Refrigerate can of coconut milk, 8 hours or overnight.
Place metal mixing bowl and beaters in the refrigerator or freezer 1 hour before making whipped cream.
Open can of coconut milk, taking care not to shake it. Scoop coconut cream solids into cold mixing bowl. Reserve remaining liquid for another use.
Beat coconut cream using electric mixer with chilled beaters on medium speed; turn to high speed. Beat until stiff peaks form, 7 to 8 minutes. Add sugar and vanilla extract to coconut cream; beat 1 minute more. Taste and add more sugar if desired.