Whisk together first 4 ingredients in a Dutch oven over medium heat, stirring constantly, 15 to 20 minutes or until mixture thickens and coats a spoon. Do not boil.
Stir about one-fourth of hot milk mixture gradually into eggs; add egg mixture to remaining hot mixture, stirring constantly. Cook 4 minutes; remove from heat. Stir in half-and-half and vanilla, and cool completely. Cover and chill at least 8 hours.
Pour into freezer container of a 4-quart electric ice-cream maker. Freeze according to manufacturer's instructions. Serve immediately, and garnish, if desired, or remove container from ice-cream maker, and place in freezer 15 minutes. Transfer to an airtight container, and freeze 2 hours or until firm. Store leftover ice cream in an airtight container.