Heat milk to 100–110°F (38–43°C). In stand mixer bowl, combine warmed milk, instant yeast, sugar, sourdough discard, egg, melted butter, and salt. Stir briefly to combine.
Add 3 cups flour and mix with dough hook on low speed for 2 minutes until incorporated. Increase to medium speed and knead for 8–10 minutes until dough pulls away from sides. Add remaining flour 1 tablespoon at a time if sticky.
Shape dough into a ball and place in a greased bowl. Cover and let rise in a warm place for 1–1.5 hours until doubled in size.
In a small bowl, mix brown sugar, cinnamon, and nutmeg. Set aside. Soften butter to room temperature.
Punch down dough and roll into a 12x18 inch rectangle on a floured surface. Spread softened butter evenly over dough, leaving a 1/2-inch border on one long edge. Sprinkle cinnamon-sugar mixture over the butter.
Starting from the long edge opposite the clean border, roll dough tightly into a log. Pinch the seam to seal. Cut into 12 equal rolls using unflavored dental floss or a sharp knife.
Arrange rolls cut-side up in a greased 9x13 inch baking dish, about 1/4 inch apart. Cover and let rise in a warm place for 30–45 minutes until puffy and touching.
Preheat oven to 350°F (175°C). Remove plastic wrap and bake rolls on center rack for 22–27 minutes until golden brown. Tent with foil if browning too quickly. Cool for 10–15 minutes.
Beat softened cream cheese until smooth. Add powdered sugar and mix until incorporated. Add milk, vanilla, and salt, beating until silky and spreadable. Adjust consistency with more milk or sugar as needed.
Spread frosting generously over warm rolls. Serve immediately while warm for the best experience.