Trim fat from meat. Cut meat into 1-inch pieces; set aside. Coat a 4- to 5-quart Dutch oven with cooking spray; heat Dutch oven over medium heat. Add mushrooms, onion, and celery. Cook about 5 minutes or until vegetables are light brown, stirring occasionally. Remove cooked vegetables from pan. Add meat and oil to Dutch oven. Cook over medium-high heat until meat is brown, stirring occasionally. Drain off fat.
Add cooked vegetables, broth, wheat berries, parsnip, carrot, dried thyme (if using), dried oregano (if using), and pepper to meat in Dutch oven. Bring to boiling; reduce heat. Simmer, covered, about 1 3/4 hours or until meat, wheat berries, parsnip, and carrot are tender, stirring occasionally.
Stir tomatoes, fresh thyme (if using), and fresh oregano (if using) into meat mixture; heat through.