In a large bowl, whisk together the warm eggnog and yeast. Let it sit for 5 to 10 minutes until it becomes foamy.

Add the granulated sugar, egg, and melted butter to the yeast mixture. Whisk until well combined.

Gradually stir in the flour and salt until a shaggy dough forms.

Turn the dough onto a floured surface and knead for 5 to 7 minutes until smooth and elastic. If the dough is too sticky, add flour one tablespoon at a time.

Place the dough in a greased bowl, cover with a towel, and let it rise in a warm spot for 60 minutes, or until doubled in size.

Punch the dough down and roll it out into a 12x18 inch rectangle on a floured surface.

Spread the softened butter over the dough, then sprinkle evenly with the brown sugar and cinnamon.

Roll the dough tightly into a log, starting from the long edge. Use a sharp knife or unflavored dental floss to cut into 12 equal slices.

Place the rolls into a greased 9x13 inch baking dish. Cover and let rise for another 30 minutes.

Whisk the powdered sugar, eggnog, and vanilla together until smooth. Drizzle over the rolls while they are still slightly warm.