Combine milk and chocolate milk in a medium saucepan over low heat. Scald
but do not allow to boil.
Combine eggs, sugar in a small bowl; using an electric mixer beat until
thick and pale in color. Gradually pour about 1/3 of the hot milk into the bowl
as you beat. Turn off beater. Using a wooden spoon gradually stir the egg mixture
back into the warm milk in the saucepan. Replace pan on stove.
Combine whipping cream and coffee liqueur; stir into pan. Stir and cook
eggnog over low heat until mixture thickens and is smooth. DO NOT ALLOW TO BOIL.
Remove from heat.
Combine rum and spices; stir into hot eggnog. Cover tightly and refrigerate
Serve with grated or curled chocolate and/or nutmeg on top.