Heat the eggnog in a small saucepan or the microwave until it's warm but not boiling (about 100F or 38C). Mine took about 35 seconds in the microwave. Add the yeast to the warm eggnog and let sit for 10 minutes. It should form bubbles and the yeast should expand. If you don't see bubbles, then your yeast is no longer active and won't work.
In a large bowl whisk together the flour, sugar, salt & nutmeg. Then stir in the egg, melted butter, and eggnog & yeast using a large wooden spoon or rubber spatula until combined. It will look shaggy. On a lightly floured flat surface working with floured hands, knead the dough for about 5 minutes until it's smooth and elastic in consistency.
Grease a large bowl, place the dough inside and cover with clingfilm. Allow the dough to rise for about 1 to 2 hours or until the dough is doubled in size. If your kitchen is cold, this process will take longer.
Once the dough has doubled in size, punch it down to release the air. On a floured surface using a floured rolling pin, roll the dough into a rectangle shape about 10 inches by 14 inches. Then spread the very soft butter onto your dough - it needs to be very soft or else you can rip your dough.
In a small bowl, combine the remaining ingredients for the cinnamon sugar filling (brown sugar, granulated sugar, cinnamon and nutmeg). Then sprinkling the coating over your dough. It will make quite a thick layer. Then starting from the long side of the dough (the 14 inch side of the rectangle), roll it up into a large log and pinch the seal closed with your fingers. Either using non-flavored dental floss or a very sharp knife, cut the log into 9-12 slices. (9 pieces for large cinnamon rolls or 12 pieces for medium sized)
Grease a 9x13 inch baking pan very well, and place your cinnamon rolls in the pan. If made only 9 rolls, you can place them in a well greased 9 inch pie plate instead.
If baking the rolls the next morning, cover the baking pan/pie plate with clingfilm and place in the fridge. The next morning when ready to bake, remove the pan from the fridge and allow the rolls to come to room temperature. Allow the rolls to sit for at least 30 minutes to warm up. Then preheat the oven to 350F degrees and bake for 22-25 minutes, or until the tops are starting to turn golden.
If baking the rolls straight through, after placing the cinnamon rolls in their greased pan allow, cover with clingfilm and allow to rest for about 20 minutes to continue rising. Then turn on the oven to 350F, and once the oven has preheated bake the rolls for 22-25 minutes or until the tops are starting to turn golden.
Make the glaze by whisking together the eggnog, powdered sugar, and optional rum extract until no lumps remain. Then pour the glaze over the warm rolls and enjoy.