Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan.

In a small mixing bowl, sift together the flour, baking powder, salt, and cinnamon or nutmeg and set aside.

In a medium mixing bowl, whisk the granulated sugar, eggnog, unsweetened apple sauce, rum, vegetable oil, vanilla extract, and rum extract until well combined.

Whisk in the egg until just incorporated.

Gradually fold the dry ingredients into the wet mixture using a spatula, being careful not to over-mix.

Pour the batter into your prepared loaf pan, smoothing the top.

Bake for about 55 minutes, or until a toothpick inserted in the center comes out clean.

Let the loaf cool in the pan for 15 minutes before transferring to a wire rack.

Prepare the glaze by combining the powdered sugar, rum, vanilla extract, and eggnog until smooth.

Pour the glaze over the loaf, letting it drizzle down the sides, then slice and serve.