Stir sugar, cream, and milk into a saucepan over low heat until sugar has dissolved. Remove from heat.
Stir in vanilla extract and chill mix thoroughly – I like to chill mine overnight.
Pour cold ice cream mix into an ice cream maker, turn on the machine, and churn according to manufacturer's directions, 20 to 25 minutes.
Place in freezer to harden 2 to 3 hours.