Preheat oven to 350°F. Spray a 9×5-inch loaf pan with nonstick cooking spray.
To a large bowl, add beaten eggs, granulated sugar, eggnog, melted butter, and vanilla extract. Whisk until fully combined.
In a separate medium bowl, whisk together flour, baking powder, kosher salt, and nutmeg.
Add the dry ingredients to the wet ingredients. Stir gently until just combined; do not overmix.
Pour the batter into the prepared loaf pan.
Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs but no wet batter. If the top is browning too quickly, loosely cover with foil during the last 15 minutes of baking.
Let the bread cool in the pan for 10 minutes, then remove it and transfer to a wire rack to cool completely.
While the bread cools, whisk together confectioners' sugar, eggnog, and vanilla extract until smooth. The glaze should be pourable but not runny. If it’s too thick, add a splash more eggnog; if too thin, add a bit more sugar.
Drizzle the glaze over the cooled bread.