Heat olive oil in a large pot over high heat. Dry the beef using paper towels, season with salt and pepper, then brown in batches. Set aside.
If needed, add more oil to the pot. Sauté onion and garlic for 2 minutes.
Introduce carrots and celery, and cook until onions turn translucent.
Mix in flour gradually, then pour in beef broth while stirring continuously.
Incorporate the beer/wine, water, tomato paste, bay leaves, and thyme. Return the beef to the pot.
Cover and let it simmer on medium-low heat for around 1 hour 15 minutes, or until the beef softens.
Add potatoes and peas, continuing to simmer for another 20 minutes without the lid. Introduce the cooked mushrooms in the last 5 minutes.
Once the beef and potatoes are tender, adjust seasoning, garnish with parsley, and serve with crusty bread or garlic bread.