Heat a 5 qt stock pot over medium-high heat. Add pancetta and cook for a few minutes. Add the cubed steak, brown on all sides. You may want to brown the meat in batches. If it gets too crowded in the pot it will steam instead of brown and the browning is crucial to the flavor of the soup.
After all steak is browned, remove it from pot, but leave the pancetta. Add the onions and saute for about 5 minutes over medium high heat. Add the tomato paste and the meat back in pot and cook for another 5 minutes.
Add the stock and the seasonings. Simmer at a steady bubble for 30 minutes. At this point taste and see if the soup needs salt and pepper.
Add the potato, celery and parsnips and cook for another 30 minutes or until vegetables are tender. Then add peas and corn, heat and serve.