Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Season the steak with salt and pepper and cook, turning once, until well browned.
Transfer the steak with 1 bay leaf and the clove-studded onion to a large pot, with a tight-fitting lid, and cover with water by 1 inch. Bring to a boil, lower the heat, and simmer, covered, until tender, about 1 1/2 hours. Remove from the heat and cool the meat in the liquid for about 30 minutes. Transfer meat to a platter and cover, to keep warm. Reserve 2 cups of the cooking liquid. (Stew may be made up to this point 1 day ahead.)
Meanwhile, return the skillet to medium-high heat and heat the remaining 3 tablespoons oil. Add the remaining bay leaf, peppers, garlic, onion, oregano, and cumin and cook, stirring, until softened and fragrant, about 8 minutes. Add the tomato paste and cook, stirring, until dark red, about 1 minute more. Add the 2 cups reserved liquid, tomatoes, and olives and bring to a boil. Lower the heat and simmer until slightly thickened, about 10 minutes.
While the vegetables are cooking, pull the steak into shreds. Add the steak and peas to the vegetable mixture and cook, stirring, until just heated through. Season with salt and pepper, to taste. Serve with white rice.