Beat eggs in a heavy saucepan; add sugar, salt, and 2 cups half-and-half. Cook over medium heat, stirring constantly until smooth and thickened. (Mixture should coat a metal spoon.) Remove custard from heat, and stir in vanilla. Cool completely.
Combine custard and remaining half-and-half; mix well. 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.