Refrigerate the can of coconut milk for 8 hours to overnight.

Place a metal mixing bowl and beaters in the refrigerator or freezer 1 hour before making whipped cream.

Open the can of coconut milk, taking care not to shake it. Scoop coconut cream solids into the cold mixing bowl. Reserve remaining liquid for another use.

Beat coconut cream with an electric mixer using the chilled beaters on medium speed; then increase to high speed. Beat until stiff peaks form, 7 to 8 minutes. Add sugar and vanilla; beat for 1 minute more. Taste and add more sugar if desired.