Mix warm milk, 2 tbsp brown sugar, and yeast; let sit until foamy (~5 min).
Add remaining brown sugar, melted butter, eggs, salt, ginger, nutmeg, and 1 cup flour; beat 1 min. Add 3 cups flour; knead until soft, tacky, and passes windowpane test.
Let dough rise in a greased bowl, covered, for 2 hours or until doubled.
Roll dough into a 10×16-inch rectangle; spread butter-molasses mixture, sprinkle spice-sugar, then roll tightly and cut into 12 rolls.
Arrange rolls in prepared pan, cover, and let rise until doubled (~1 hour). Bake at 350°F (177°C) for 25–28 min, tenting with foil after 15 min.
Make icing by beating cream cheese, butter, sugar, vanilla, and cinnamon; spread over warm rolls and serve.
Notes
For best results, ensure dough is properly kneaded and rises in a warm environment.