Pour oil into a 12-inch nonstick frying pan over medium-high heat. When hot, add lamb chops and cook, turning once, until browned on both sides, about 4 minutes total. Transfer to a plate.
Add onion and garlic to pan; stir often until limp, about 4 minutes. Add cinnamon and cumin; stir until fragrant, 1 minute longer. Stir in broth, tomato paste, apricots, and garbanzos; bring to a simmer. Return lamb chops to pan.
Cover and simmer, turning chops once, until apricots are plump and chops are barely pink in the center (cut to test), 10 to 12 minutes.
Set two lamb chops on each of four plates or in shallow bowls. Spoon garbanzo mixture around meat. Sprinkle with parsley.