With a sharp knife, cut the filet crosswise into 1-inch-thick slices

Salt and pepper the filets on both sides

In a large, heavy-bottomed pan on medium-high heat, sauté the slices of beef in batches with 2 to 3 tablespoons oil until browned on the outside and very rare inside, about 2 to 3 minutes on each side

Remove the filets from the pan and set aside on a platter

In the same pan, sauté the bacon on medium-low heat for 5 minutes, until browned and crisp

Remove the bacon and set it aside

Drain all the fat, except 2 tablespoons, from the pan

Add the garlic and cook for 30 seconds

Deglaze the pan with the red wine and cook on high heat for 1 minute, scraping the bottom of the pan

Add the beef stock, tomato paste, thyme, 1 teaspoon salt, and ½ teaspoon pepper

Bring to a boil and cook uncovered on medium-high heat for 10 minutes

Strain the sauce and return it to the pan

Add the onions and carrots and simmer uncovered for 20 to 30 minutes, until the sauce is reduced and the vegetables are cooked

With a fork mash 2 tablespoons butter and the flour into a paste and whisk it gently into the sauce

Simmer for 2 minutes to thicken

Meanwhile, sauté the mushrooms separately in 1 tablespoon butter and 1 tablespoon oil for about 10 minutes, until browned and tender

Add the filet of beef slices, the mushrooms, and the bacon to the pan with the vegetables and sauce

Cover and reheat gently for 5 to 10 minutes

Do not overcook. Season to taste and serve immediately