Grease a 10 inch (25 centimeter) cast iron skillet with butter.
In a medium bowl, evenly combine the brown sugar and cinnamon.
Lightly dust a large work surface with flour.
Roll the risen dough into a rectangle about 14 inches (35.5 centimeters) long and 11 inches (28 centimeters) wide.
Evenly spread 4 tablespoons (60 grams) softened butter over the surface of the dough.
Sprinkle the brown sugar cinnamon mixture over the butter in an even layer, leaving about 1/2 inch (1.25 centimeters) free across the long edges.
Roll up the rectangle tightly from long side to long side and pinch the seam to seal.
Using a sharp knife, cut the log into 9 equal rolls.
Place the rolls cut side up in the prepared cast iron skillet. Cover lightly with a towel and allow to rest at room temperature until puffed, 30 minutes to 1 hour.
Preheat oven to 350˚F (180˚C).
Place the cast iron skillet on a rimmed baking sheet (to protect the oven in case any of the brown sugar bubbles over) and place the baking sheet in the preheated oven.
Bake the rolls until deeply golden over the top and the center is cooked through, 25-30 minutes.
While the rolls are baking, prepare the cream cheese frosting.
In a medium bowl, beat together the cream cheese and butter until smooth.
Beat in the powdered sugar until incorporated, then the vanilla extract and slowly pour in the milk to form a light and smooth frosting.
Once the cinnamon rolls are baked through, remove from the oven and allow to rest in the skillet for 5 minutes.
Spread the cream cheese frosting over the rolls and serve warm.