Trim the lamb and cut it into approximately 1-inch cubes.
Heat the olive oil in a medium Dutch Oven or other heavy pot over medium-high heat. Add the lamb and cook until browned on each side, about 5 minutes. Add the onion; cook until softened, about 10 minutes.
Deglaze the pan by pouring in the balsamic vinegar, which will loosen any browned bits that are stuck to the bottom of the pan. Stir in the next 8 ingredients (through the cloves). Bring to a simmer, then reduce heat to low and cook, covered, for 60 minutes, or until lamb is fork-tender. Season with salt. Remove cover and simmer 15 minutes, or until liquid has reduced to a thick sauce.
Combine rice and water in a medium pot. Bring to a boil, then reduce heat to low and cook, covered, for 20 minutes. Remove from heat and fluff with a fork.
Serve the braised lamb over the rice. Sprinkle with chopped parsley.