Season the beef cubes with salt and pepper, then dredge them in flour, shaking off any excess.

Heat the olive oil in a large pot or Dutch oven over medium-high heat. Brown the beef in batches, ensuring each piece has room to sear properly. Set browned beef aside on a plate.

In the same pot, add the onions and garlic, cooking until softened. Add more oil if needed. Then add the carrots and celery, cooking for a few minutes more.

Add a splash of beef broth to deglaze the pot, scraping up any browned bits from the bottom. Return the beef to the pot along with any accumulated juices.

Stir in the remaining beef broth, tomato paste, Worcestershire sauce, dried thyme, bay leaves, and mushrooms (if using). Bring to a simmer.

Once simmering, reduce the heat to low, cover, and let it cook for about 1.5 hours, stirring occasionally. After this time, add the cubed potatoes and continue to simmer covered for another 30 minutes, or until the beef and potatoes are tender.

Add the frozen peas and cook for an additional 10 minutes. Check the seasoning and adjust with more salt and pepper if necessary. Remove the bay leaves.

Garnish the casserole with chopped fresh parsley before serving. This dish is hearty enough to serve on its own or with some crusty bread for dipping into the gravy.