In a large pot or Dutch oven, heat the olive oil over medium-high heat. Season the short ribs with salt and pepper, then add them to the pot. Brown the ribs on all sides, about 8-10 minutes. Remove the ribs and set aside.
In the same pot, add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened. Add the minced garlic and sliced mushrooms, cooking for another 3-4 minutes until the mushrooms are tender.
Return the browned short ribs to the pot. Pour in the beef broth, then add the thyme, rosemary, and bay leaf. Bring the mixture to a boil, then reduce the heat to low. Cover and let simmer for 2 to 2.5 hours, or until the meat is tender and falling off the bone.
Once the short ribs are tender, remove them from the pot. Discard the bay leaf. Shred the meat from the bones and return the meat to the soup. Stir in the frozen peas and cook for an additional 5 minutes. Adjust seasoning with salt and pepper as needed.
Serve the soup hot, garnished with fresh parsley.
Notes
For a richer flavor, consider adding a splash of red wine after sautéing the vegetables and before adding the broth.
For a lighter version, substitute turkey or chicken short ribs and use low-sodium broth.