Heat oven to 350 F and grease the bottom and sides of a 9x5-inch loaf pan.
In a large bowl using a whisk, beat eggs.
To the eggs, add sugar, eggnog, melted butter, rum (extract), and vanilla extract. Blend well until smooth.
To the wet ingredients, add flour baking powder, salt, and nutmeg. Using a rubber spatula stir just until dry ingredients are moistened.
Pour batter into greased pan and bake for 45-50 minutes or until a toothpick inserted in the center comes out clean.
Let cool in the pan for 10 minutes set on a wire rack, then remove from pan and let cool completely.
Combine powdered sugar, rum, and eggnog. Add one tsp at a time until the glaze is smooth and thick. Pour over bread, sprinkle with nutmeg or cinnamon, and let set before serving.