Warm up eggnog to about 110°F (too hot will kill the yeast, too cold will not activate yeast).
In the bowl of an electric mixer, beat butter, sugar and vanilla until fluffy. Add eggs one at a time until incorporated. Gradually add the flour and salt until combined.
Pour the milk/yeast mixture in the bowl and using the dough hook, mix well until well incorporated. Dough should be smooth and pulling away from the sides of the bowl, and not too sticky.
Place dough into an oiled bowl, cover. Turn off oven and place covered bowl in oven. Allow to rise for about an hour, or until dough has doubled.
Turn out dough on a lightly floured surface. Dust with flour. If dough is sticky, work just a little four into it so that it is easy to roll out. Use a rolling pin to roll into a 16x20 rectangle.
Preheat oven to 200°F degrees. Grease a 9x13 inch baking pan.
To Make Filling:
Combine brown sugar, cinnamon and nutmeg in a bowl.
Spread the softened butter evenly over the surface of the dough, leaving about ¼ of the dough around the edge. Sprinkle the brown sugar mixture over the butter.
Working carefully, from the long edge, tightly roll the dough into a log. The roll should be about 18 inches in long. I usually cut off the two tapered ends. Cut the roll into eight slices. You might find it easier if you use a piece of floss, or use a serrated knife..
Place the cut rolls in the prepared pan. Cover them with a damp towel. Turn off oven and place rolls in oven. Let them rise again for another 30 minutes until they double in size.
Remove rolls from oven and preheat oven to 350°F degrees. When oven is preheated, bake for 20-25 minutes or until light golden brown.
While the rolls are baking make the icing. In a small saucepan, melt the butter and 2 tablespoons of eggnog. Stir in nutmeg.
Whisk together until butter is melted. In a bowl, mix the softened cream cheese with the butter mixture. Add in the powdered sugar. Whisk together until smooth. Add additional tablespoon of eggnog if icing is too thick.
When the rolls are done, pour half of the icing over them. Allow to cool and finish with the remaining icing.
To make ahead, follow recipe through Step 10, place rolls in the prepared pan, then cover rolls with plastic wrap and refrigerate, up to overnight. When ready to bake, remove from fridge and allow to come to room temperature (about an hour) then continue with recipe. Cinnamon rolls adapted from Jo CooksEggnog glaze adapted from Allrecipes