In a medium mixing bowl, use a hand mixer or your stand mixer on low speed to combine the milk and sugar until the sugar is dissolved, about 1 - 2 minutes. Stir in the cream and vanilla.
Turn the ice cream machine on and pour the mixture into the freezer bowl. Let mix until thickened, about 20 - 25 minutes.
The ice cream will have a soft, creamy texture. If a firmer consistency is desired, transfer the ice cream to an airtight container and place in the freezer for about 2 hours.
Remove from freezer about 15 minutes prior to serving.