Heat a frying pan over medium-high heat. Coat the bottom with 3 tablespoons oil; add steak and cook, turning as needed, until browned, 5 to 7 minutes. Transfer steak to a 3-quart baking dish.
Add remaining 2 tablespoons oil to the frying pan. Sauté mushrooms, onion, and garlic in the hot oil until softened, about 5 minutes. Remove from the heat.
Add red wine, tomato paste, flour, salt, pepper, and bay leaf to the pan. Whisk in beef broth until well combined, then pour mixture over beef. Cover the baking dish with aluminum foil.
Preheat the oven to 350 degrees F (175 degrees C).
Bake in the preheated oven until beef is tender, 45 minutes to 1 hour.