Combine cornstarch and 1/4 cup milk; stir until smooth. Combine scalded milk, 2 cups sugar, eggs, and cornstarch mixture in a large Dutch oven; stir until well blended, and set aside.
Sprinkle remaining sugar evenly in a 10-inch cast-iron skillet; place over medium heat. Caramelize sugar by constantly stirring with a wooden spoon. Remove sugar from heat, and gradually pour into milk mixture in Dutch oven.
Cook over medium heat, stirring constantly, until smooth and thickened. Remove from heat; cool. Stir in half-and-half and vanilla.
Pour into freezer can of a 1- gallon hand-turned or electric freezer. Freeze according to manufacturer's instructions. Let ripen at least 1 hour before serving.