For the Marinade: Combine brown sugar and balsamic vinegar and chops.
Marinate chops about 30 minutes. Drain off marinade to a cup and set it aside. Preheat Oven to 350 degrees F. Transfer pork chops to plate. Sprinkle lightly with black pepper. Melt butter in a heavy ovenproof skillet over medium-low heat. When melted, increase heat to medium-high. Place chops in skillet and brown them on each side for about 3 minutes per side. Place skillet in center of oven.
Make sauce. For the Cherry Cream Sauce: Place broth, cherries and reserved marinade in a saucepan. Bring to a boil. Reduce heat and simmer until cherries are tender and sauce is slightly reduced. Add 1 Tablespoon butter and cream. Transfer pork to plates; top with sauce.