To the bowl of a stand mixer fitted with the paddle attachment, add warm eggnog, 1 tablespoon of granulated sugar, and the yeast. Mix briefly, then let sit until the yeast is foamy, about 5 minutes.
Add the eggs, butter, remaining 4 tablespoons of sugar, all-purpose flour, bread flour, and salt. Switch to the dough hook attachment and mix on low speed until combined.
Continue kneading on medium speed until the dough is smooth, about 5 minutes.
Spray a medium bowl with nonstick cooking spray. Place the dough in the bowl and rotate to grease all sides. Cover with a towel or plastic wrap and let rise in a warm place until doubled in size, 1-2 hours.
Once the dough has doubled, transfer it to a lightly floured work surface. Roll into a 10×15-inch rectangle, about ¼-inch thick.
In a small bowl, mix together the softened butter, light brown sugar, cinnamon, nutmeg, and salt until well combined.
Spread the filling mixture evenly over the dough, covering the entire surface.
Spray a 9×9-inch baking dish with nonstick cooking spray.
Starting from the long edge, tightly roll the dough into a log. Using a very sharp knife, cut the log into 9 even rolls. Place the rolls in the prepared baking dish, filling side up. Cover with plastic wrap and let rise in a warm place until doubled in size, about 1 hour.
Preheat the oven to 325°F.
Bake the rolls for 35-40 minutes, or until the edges are lightly golden and the centers are cooked through.
Let the rolls cool slightly before frosting.
To make the frosting, add cream cheese, butter, and confectioners’ sugar to the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed until smooth.
Add eggnog, 1 tablespoon at a time, until the desired consistency is reached.
Switch to the whisk attachment and mix on high speed for 4-5 minutes until the frosting is light and fluffy.
Spread the frosting generously over the warm rolls and serve.