Preheat your oven to 160°C (320°F).
In a large ovenproof casserole dish, heat the olive oil over medium-high heat.
Add the beef stew meat and cook until browned on all sides. Remove the meat from the dish and set it aside.
In the same casserole dish, add the chopped onions, garlic, carrots, and celery. Cook for about 5 minutes, until the vegetables start to soften.
Sprinkle the flour over the vegetables and stir well to coat them. Cook for another 2 minutes to remove the raw taste of the flour.
Pour in the red wine (if using) to deglaze the pan, scraping up any browned bits from the bottom of the dish.
Return the browned beef to the casserole dish, add the sliced mushrooms, bay leaves, dried thyme, and season with salt and pepper. Stir everything together.
Pour in the beef broth, making sure the meat and vegetables are mostly covered. If needed, you can add a bit more broth or water.
Cover the casserole dish with a lid or foil and place it in the preheated oven. Let it cook for about 2 hours, or until the beef is tender and can be easily pierced with a fork.
About 30 minutes before the casserole is done, add the peeled and chopped potatoes to the dish. Stir them into the liquid.
During the last 5 minutes of cooking, add the frozen peas.
Once the beef is tender, remove the casserole dish from the oven and discard the bay leaves.
Serve the beef and mushroom casserole hot, garnished with chopped fresh parsley.Enjoy your delicious beef and mushroom casserole!