Preheat oven to 350°F. Butter and flour a 9 x 5 inch loaf pan or spray with baking spray. Set aside.
In a medium-size mixing bowl, whisk together flour, baking powder, baking soda, salt, nutmeg and cinnamon.
In a separate bowl, whisk together eggnog, sugar, oil, vanilla and rum extracts with the eggs until fully combined. Add the wet ingredients to dry ingredients, mixing just until fully moistened.
Pour the batter evenly into pan. Bake for 50-60 minutes until golden and a tester inserted into the center comes back clean.
Cool in the pan for 20 minutes, then remove to a cooling rack to cool completely.
To make the Glaze: In a small mixing bowl whisk together powdered sugar, vanilla and rum extracts, nutmeg and enough eggnog to reach drizzle consistency. Drizzle slowly over warm bread, repeating until all is used.
Store Eggnog Bread chilled in the refrigerator an airtight container for up to 5 days.