Beat eggs at medium speed on an electric mixer until frothy. Gradually add sugar, beating until thick. Heat half and half in a 3-quart saucepan over low heat until hot. Gradually stir about
one-fourth of hot mixture INTO eggs; add remaining hot mixture, stirring constantly. Cook over low heat until mixture is slightly thickened and reaches 165 degrees. Remove form heat, and stir in chocolate syrup and remaining ingredients. Cool in refrigerator. Pour into freezer can on a 1 gallon freezer. Freeze according to manufacturer's instructions. Let ripen at at least 1 hour. Yield about 1 gallon.