Cut bacon into lardons (sticks, 1/4 inch thick and 1 1/2 inches long). Simmer the bacon for about 10 minutes in 1 1/2 quarts of water. Drain and dry.
Preheat the oven to 450 degrees. In a large Dutch oven, saute the bacon in the olive oil over medium heat for about 2-3 minutes, until slightly browned. Using a slotted spoon or tongs, remove the bacon to a side dish. Reheat the Dutch oven until fat is almost smoking before you sauté the beef.
Dry the stewing beef in paper towels; it will not brown if it is damp. Sauté it, a few pieces at a time, in the hot oil and bacon fat until nicely browned on all sides. Set it aside with the bacon.
In the same fat, brown the sliced vegetables and season with salt and pepper. Pour out the sautéing fat if necessary. Once the vegetables are browned, return the beef and bacon to the pan. Sprinkle the flour over the beef and toss to coat. Set the Dutch oven, uncovered in the middle position of the oven for 4 minutes. Toss the meat and return to the oven for another 4 minutes. This is what helps the meat to get a nice brown crust. Remove the Dutch oven and place on the stove. Turn the oven down to 325 degrees.
Stir in the wine and add enough beef stock so that the meat is barely covered. Add the tomato paste, garlic, thyme, and bay leaf. Bring to a simmer on the stove. Cover the Dutch oven and place in the lower third of the oven. Regulate heat so the liquid simmers very slowly for about 2 1/2 to 3 hours. The meat is done when a fork pierces it easily.
While the beef is cooking, prepare the onions and mushrooms.