1. Heat half-and-half in a medium saucepan over moderate heat (do not boil).
2. Whisk together eggs, sugar, vanilla, and nutmeg in a large bowl. Gradually whisk in 1 cup hot half-and-half in a slow stream. Whisk egg mixture into remaining half-and-half in saucepan. Cook over low heat, stirring, until it thickens and registers 170 degree F on an instant-read thermometer, about 2 minutes.
3. Blend in small batches in a blender until frothy. Divide rum among 8 heat-proof glasses and top with eggnog. Dust tops with nutmeg. Makes 8 servings.