Take your beef and pat it dry with paper towels, season the beef with the salt and pepper.
In a large dutch oven or pot heat 1 tablespoon of oil over medium-high heat. Add half the beef to the pan and brown the beef on all sides. Remove the beef from the pan and repeat this with 1 tablespoon of oil and beef. Once you have browned the second batch of beef remove it from the pan to a plate and cover it with foil.
Add the last 1 tablespoon of oil to the same pot and saute the onion, carrot, and mushrooms until the onions are translucent. Add in the garlic and celery, cook until the garlic is golden. Add in the tomato paste and stir until it has coated all the vegetables.
Stir in the beef broth, thyme, bay leaves and beef. Bring the stew up to a boil then cover and cook on medium-low heat for 1 hour.