Combine brown sugar and jerk seasoning. Rub mixture over both sides of pork chops; let stand while cooking peppers.
Heat oil in large skillet over medium heat. Add peppers and salt; cook, stirring occasionally, until tender, 5 minutes. Remove to a plate; cover to keep warm.
In same skillet over medium-high heat, cook pork chops, turning once, until browned and just cooked through, 4-5 minutes per side. Remove pork to plate with peppers.
Add rum to skillet; bring to a boil. Cook 30 seconds, scraping bits on bottom of skillet. Return peppers, pork chops and any juices on plate to skillet; heat through, about 1 minute. If desired, garnish with cilantro.