Arrange 12 dinner rolls in the prepared baking dish.
Melt butter in a saucepan over medium-low heat. Add brown sugar, pudding mix, milk, and cinnamon to melted butter; stir until smooth. Pour pudding mixture over rolls; top with remaining 12 rolls. Allow rolls to rise for 3 hours.
Preheat oven to 375 degrees F (190 degrees C).
Bake in the preheated oven until rolls are cooked through, 30 to 35 minutes. Cool for 15 minutes before serving.