In a medium mixing bowl, use a hand mixer on low speed to combine the milk and granulated sugar until the sugar is dissolved, about 1 to 2 minutes. Stir in the heavy cream and vanilla.
Turn the machine on; pour the mixture into freezer bowl, and let mix until thickened, about 20 to 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 freezer for about 2 hours.
Remove from freezer about 15 minutes before serving.