Combine sugar, yeast, salt, and 4 cups of the flour in the work bowl of a stand mixer fitted with the paddle attachment. Beat on low speed until just combined, about 15 seconds.

With mixer running on low speed, add eggnog, sour cream, butter, and egg. Continue beating until dough forms, 1 to 2 minutes.

Switch to a dough hook attachment. Beat on medium-low speed until dough is smooth and elastic, 6 to 9 minutes; gradually add remaining 1/2 cup flour, 1/2 to 1 teaspoon at a time, if necessary.

Place dough in a large bowl greased with cooking spray and turn to coat. Cover with a clean kitchen towel and let rise in a warm draft-free place until dough has doubled in size, 2 to 3 hours.

Spray a 13- x 9-inch pan with cooking spray. Lightly punch down dough. On a lightly floured surface, roll dough into an 18- x 10-inch rectangle.

For the filling spread 1/2 cup of butter over the dough. In a small bowl, stir together brown sugar, cinnamon, and nutmeg. Sprinkle evenly over butter.

Starting with one long side, roll dough into a log; pinch seam to seal. Slice into 12 rolls.

Place rolls in the prepared pan. Cover, and let rise in a warm draft-free place until doubled in size, 1 hour to 1 hour and 15 minutes.

Preheat the oven to 350 degrees F (175 degrees C). Bake in the preheated oven, uncovered, until golden brown, 25 to 30 minutes. Let cool in the pan on a wire rack for 15 minutes.

Add cream cheese and butter to the bowl of a stand mixer fitted with the paddle attachment; beat on medium speed until smooth, 1 to 2 minutes.

Add powdered sugar, eggnog, and vanilla. Beat on medium speed until smooth, about 1 minute.