Brown beef with vegetable oil and butter over high heat in large cooking pot. Add chopped yellow onion and carrots, and continue to brown for approximately 3 minutes. Add flour and cook for an additional 3 minutes. Carefully add cognac and ignite with a match. This will produce a large flame, so be very careful. Let the flame burn out, and add red wine, beef broth, chopped shallots, garlic, tomato paste, bouquet garni, salt, pepper, and thyme. Cover, reduce heat and simmer for approximately 2 hours. While the beef is simmering, begin prepping the other items.
Preparation for white onion, potatoes, and bacon (lardons)
Cook the white onions in pot with butter. Add just enough water to barely cover the onions. Cook until light brown over medium heat. Set aside. Boil the potatoes with water and salt in large pot until cooked, approximately 15-20 minutes. Drain and set aside. Cut bacon into strips (lardons) and place in a pot with cold water. Bring to a boil, drain and rinse under cold water. Drain well and dry. In a large skillet, cook the lardons over medium heat until brown and crisp. Let drain on paper towels. Set aside. Pour off all but 2 teaspoon of the bacon fat from the skillet; add mushrooms to the skillet and sauté. Remove and set aside. Add the cooked white onion.
When the beef is cooked, use a slotted spoon to transfer it to the serving dish. Add the potatoes, onion, mushrooms, and lardons. Skim any fat off the sauce; strain the sauce over the meat and vegetables. Garnish with chopped parsley.