Remove any bits of fat from the meat. Heat the oil in a large pot over medium high heat. Saute the meat in the oil for 10 minutes, or until browned on all sides. Remove meat and set aside.
Add the onion and tomato paste to the pot and saute over medium heat for 5 minutes, or until onion is tender, stirring often.
Return the meat to the skillet along with the beef broth, combining with the onion and tomato paste mixture. Reduce heat to low, cover and simmer for 1 to 1 1/2 hours, or until meat is tender.
Add carrots, potatoes, rosemary, thyme, bay leaf and crushed red pepper flakes and simmer, covered, for another 45 minutes. (Note: It may be necessary to add some water if the stew seems too thick.)
Finally, add the mushrooms and peas and allow beef stew to heat through, about another 10 to 15 minutes. Remove bay leaf and rosemary sprig before serving.