Heat oil in a large stockpot and add venison, cooking until evenly browned. Add onion and garlic and cook for a few minutes more. Add next 5 ingredients, bring to a boil, then reduce heat to low. Cover and simmer until meat begins to break apart easily. Add carrots, celery and beans. Cook 10 minutes. Add pasta and cook until al dente, about 10 minutes. Serve in bowls and top with Parmesan cheese.