Combine milk, cream, and sugar in a saucepan over low heat. Stir gently until the sugar is fully dissolved and the mixture is just hot, with a small ring of foam at the edge.

Remove the saucepan from heat. Add vanilla extract to the mixture and stir well. Transfer the mixture to a container that can be sealed and chill in the refrigerator for at least 2 hours, or overnight for best results.

Once chilled, pour the mixture into an ice cream maker. Churn according to the manufacturer's instructions, usually for about 20 to 25 minutes, until the ice cream is softly frozen.

Serve the ice cream immediately for a soft-serve consistency, or transfer to a freezer-safe container, cover with plastic wrap, and freeze for 2 to 3 hours to allow the ice cream to firm up.