In a 4-quart Dutch oven or kettle cook the meat, half at a time, in hot oil over medium-high heat until brown. Drain fat.
Stir in water, broth, bay leaves, oregano, marjoram, salt, and pepper. Bring to boiling. Stir in carrot, celery, and pasta. Return to boiling; reduce heat. Simmer, covered, about 15 minutes or until vegetables and pasta are tender. Discard bay leaves.
Stir in spinach. Cook for 1 to 2 minutes more or just until spinach wilts.