Heat the oil in a large Dutch oven over medium heat. Add the lamb cubes and brown them on all sides for about 6 minutes. Remove the lamb and set it aside.
Add the onions to the pot and cook for 4 minutes until softened. Stir in the garlic, paprika, and caraway seeds and cook for 1 minute more.
Return the lamb to the pot. Add the bell pepper, carrots, tomato paste, beef broth, bay leaf, salt, and pepper. Bring the mixture to a boil.
Stir in the barley, then reduce the heat to low. Cover and simmer for 1 hour and 15 minutes, stirring once or twice, until the lamb is tender and the barley is cooked through.
Remove the bay leaf. Taste and adjust salt and pepper if needed. Sprinkle with parsley before serving.