Add the rest of the ingredients to the bowl: butter, eggnog, eggs, dark rum, and vanilla extract. Beat on low until ingredients begin to mesh, then increase speed to medium. Beat for another 3-4 minutes so that batter is thick and smooth.
Pour batter into the prepared bundt cake pan and bake for 65-70 minutes or until a toothpick inserted near the center comes out clean (no crumbs).
Transfer bundt cake (still in the bundt cake pan) to a wire rack to cool. Allow cake to cool completely before removing from the pan, about 1 hour.
For the Eggnog Glaze
In a small bowl, whisk together powered sugar, eggnog, cinnamon, and vanilla extract until smooth.
Check for consistency - if glaze is too thin, add 1 tablespoon of powdered sugar at a time until desired thickness is reached. If glaze is too thick, add 1 teaspoon of eggnog until glaze is workable.
Using a spoon, drizzle glaze on top of bundt cake. Allow glaze 20 minutes to set before serving.
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