Prep the oven Preheat to 350°F (175°C). Pat beef dry and season with salt and pepper.
Sear the beef In a Dutch oven, heat olive oil over medium-high. Sear beef in batches until browned (about 2 minutes per side). Set aside.
Sauté the veggies In the same pot, reduce heat to medium. Add onion, carrots, and bay leaves. Cook 5 minutes. Add garlic and tomato paste, stir until fragrant.
Build the braise Sprinkle flour over vegetables and stir. Slowly pour in wine, stirring constantly. Add mushrooms and return beef to the pot. Nestle it into the liquid.
Braise Add thyme, bring to a boil, cover tightly, and transfer to oven. Cook for 2½ to 3 hours until beef is fork-tender.
Serve Remove bay leaves and thyme stems. Serve with mashed potatoes or egg noodles for a full comfort meal.