In a large bowl or the bowl of a stand mixer, stir together the warm eggnog, yeast, and 1 tablespoon of the sugar. Let sit for 5 minutes until foamy.
Add the sourdough discard, egg, softened butter, remaining sugar, salt, nutmeg, and 3 cups of flour. Mix until a shaggy dough forms.
Knead with the dough hook on medium low for 6 to 8 minutes, or by hand for about 10 minutes, until smooth and slightly tacky. Add the remaining flour 1 tablespoon at a time only if needed.
Place the dough in a greased bowl, cover, and let rise in a warm spot for 1 to 1 ½ hours until doubled.
Meanwhile, mix the filling ingredients together until smooth and spreadable. Grease a 9 by 13 inch baking pan.
Punch down the dough and roll it into an 18 by 12 inch rectangle on a lightly floured surface. Spread the filling evenly, leaving a ½ inch border along one long edge.
Starting with the long edge without the border, roll the dough up tightly. Pinch the seam to seal and cut into 12 even rolls.
Arrange the rolls in the prepared pan, cover, and let rise for 30 to 45 minutes until puffy.
Preheat the oven to 350°F. Bake for 22 to 28 minutes, until golden brown and the center roll reads 190°F.
While the rolls bake, beat the cream cheese and butter until smooth. Add the powdered sugar, 3 tablespoons eggnog, vanilla, and nutmeg, and beat until creamy, adding more eggnog if needed.
Let the rolls cool for 10 minutes, then spread the icing over the top and serve warm.