Preheat broiler. Rub oil over pork and set on a broiler pan. Mix spices together and sprinkle evenly on both sides of meat. Broil, turning once, until browned and cooked through, about 8 minutes. Remove from pan and keep warm.
Lay plantains, cut side up, on a baking sheet and sprinkle with sugar. Broil until sugar starts to caramelize and fruit starts to soften, 4 to 8 minutes.
Serve pork chops and plantains with black beans, a dollop of sour cream, a few chile slices, and cilantro leaves.
Note: Nutritional analysis is per serving.