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.
Butterscotch pudding can be used instead of vanilla if desired.
If you let this raise overnight, keep in the refrigerator.