Combine all ingredients except the vanilla extract in a medium saucepan. Bring to a simmer over medium heat, whisking to incorporate all ingredients. Remove from heat and stir in the vanilla extract.

Making the ice cream with a machine: Place the mixture in the refrigerator to fully chill. Process through an ice cream maker to the manufacturers instructions. Spoon the ice cream into a freezer-safe container to allow to fully freeze overnight. Making the ice cream without a machine: Allow the mixture to cool to room temperature. Pour into a freezer-safe container and seal or cover with plastic wrap. Freeze until firm (6 hours to overnight depending on your freezer).