In the same pan, sauté bacon over medium-low heat 5 minutes, until browned and crisp. Remove bacon and set aside. Drain all but 2 tablespoons of fat from pan. Add garlic and cook 30 seconds.
Deglaze pan with red wine and cook on high heat 1 minute, scraping pan bottom. Add beef stock, tomato paste and thyme; season with salt and pepper. Bring to a boil and cook over medium-high heat 10 minutes. Strain sauce and return to pan. Add onions and carrots and simmer 20 to 30 minutes, until sauce is reduced and vegetables are cooked.
In a small bowl, mash 2 tablespoons butter and flour into a paste using a fork, then whisk gently into sauce in pan. Simmer 2 minutes to thicken.
Meanwhile, over medium heat, sauté mushrooms separately in 1 tablespoon butter and 1 tablespoon olive oil about 10 minutes, until browned and tender.
Add beef slices, mushrooms and cooked bacon to pan with vegetables and sauce. Cover and reheat gently, 5 to 10 minutes. If the mixture doesn't have enough liquid, add more red wine. Season to taste and serve immediately.
Recommended technique: To peel onions easily, first blanch one to two minutes in boiling water.