Heat eggnog in microwave for 40 seconds or until it's warm to the touch (about 110 degrees).
Pour eggnog into the bowl of an electric mixer and sprinkle with yeast.
Add sugar, egg, egg yolk and melted butter. Whisk until combined.
Stir in flour and salt with a wooden spoon until dough begins to form.
Knead dough by hand on a floured surface for 10 minutes or use an electric mixer with a dough hook attachment on medium speed for 8 minutes.
If dough sticks to the counter/bottom of the bowl add an additional 2 Tbsp of bread flour and continue kneading until a soft, slightly sticky ball forms.
Place dough in an oiled bowl, cover with plastic wrap and a dry, warmed towel and let it rise for 1 hour to 1.5 hours until doubled in size.
On a lightly floured surface, roll dough with a rolling pin until it is a 14 x 9 inch rectangle.
Spread softened (not melted) butter over the surface of dough. Combine brown sugar, cinnamon and nutmeg then sprinkle over buttered dough. Press spiced sugar mixture into the butter with your hands.
Tightly roll the dough into the shape of a log starting with the short side. Trim and discard uneven ends then cut dough into eight rolls with a serrated knife or non-minty floss. Fishing line also works great.
Grease a 9 x 13 baking pan and line with parchment. Arrange eggnog cinnamon rolls in the pan, cover with plastic wrap and a dry, warm towel and allow to rise for 30 to 45 minutes.
Preheat oven to 350 degrees.
Remove towel and plastic wrap from baking pan and bake eggnog cinnamon rolls for 20 to 25 minutes or until the edges are slightly golden brown. Do not overbake.
Allow to cool in pan for 5 minutes while you make the frosting.