Prep Time: 15
Cook Time: 35
Serves: Serves: 4
Melt 1 tablespoon of the butter in a heavy saucepan over medium-high heat. Add brown sugar; mix well. Add onions and rosemary; cook over medium-low heat, stirring frequently, until golden brown, 20 to 25 minutes.
Spread remaining 3 tablespoons butter over one side of each slice of bread.
Layer half of cheese slices and prosciutto over the unbuttered sides of 4 slices bread; top with onion mixture. Place remaining cheese slices over onion mixture; close sandwiches with remaining bread, butter sides up.
Heat a ridged grill pan (or nonstick skillet) over medium heat until hot. Cook sandwiches in pan (in 2 batches) 5 to 6 minutes per side or until golden brown and cheese is melted.