Pat the beef dry and season with the salt and pepper. Heat 2 tablespoons of the oil in a large Dutch oven over medium-high heat. Brown the beef in two or three batches without crowding, 3–4 minutes per side, transferring each batch to a plate.
Lower the heat to medium and add the remaining oil and the onion. Cook, scraping up the browned bits, until softened, about 5 minutes. Add the garlic and tomato paste and cook 2 minutes, stirring.
Sprinkle in the flour and stir for 1 minute. Gradually pour in the broth, stirring to prevent lumps. Add the Worcestershire, bay leaves, thyme and the beef with any juices.
Bring to a boil, then cover, reduce the heat to low and simmer gently for 1 1/2 hours, stirring occasionally.
Add the carrots, celery and potatoes. Cover and simmer 40–50 minutes more, until the beef is fork-tender and the vegetables are cooked.
Stir in the peas and cook 5 minutes. Remove the bay leaves, season to taste and sprinkle with parsley.