Heat olive oil in heavy large pot over medium-high heat. Add ground turkey and ground beef and saute until brown, about 3 minutes. Add cubed beef and garlic and saute 5 minutes. Add 2 cups water; bring to boil. Add cumin, chili powder, oregano, salt, and cayenne pepper. Reduce heat, cover, and simmer 10 minutes. Add tomato paste and sugar and simmer 5 minutes. Add tomatoes, onions, and peppers and simmer until vegetables are tender, about 30 minutes.
Add black beans, cilantro and any amount minced hot chile peppers you may desire. Add beef broth 3/4 cup at a time, until thinned to desired consistency. (Can be prepared 1 day ahead. Refrigerate uncovered until cold, then cover and keep refrigerated.) Bring chili to simmer. Ladle hot chili into bowls; top with grated cheddar cheese and serve.