Blanch the bacon to remove its smoky taste. Drop bacon slices into 2 quarts of cold water, bring to a boil, and simmer 6 to 8 minutes. Drain, rinse in cold water, and dry on paper towels.
In a large frying pan, sauté the blanched bacon to brown slightly in a little oil; set them aside and add later to simmer with the beef, using the rendered fat in browning. Brown the chunks of beef on all sides in the bacon fat and olive oil, season with salt and pepper, and put them into a heavy-bottomed Dutch oven or covered casserole pan. Cut the bacon into 1-inch pieces and add to the pan.
Remove all but a little fat from the frying pan, add the sliced vegetables and brown them, and add to the meat. Deglaze the pan with wine, pouring it into the casserole along with enough stock to almost cover the meat. Stir in the tomatoes and add the herb bouquet. Bring to a simmer, cover, and simmer slowly on the lowest heat possible, either on the stove or in a preheated 325°F oven, until the meat is tender, about 1 to 2 hours.
While the stew is cooking, prepare the onions. Blanch the onions in boiling water for 1 minute. Drain and rinse in cold water to stop the cooking. Slice the end tips off of the onions, peel the onions and score the root end with 1/4 inch cuts. Sauté onions in a single layer in a tablespoon or two of butter until lightly browned. Add chicken stock or water half way up the sides of the onions. Add a teaspoon of sugar, and season with salt and pepper. Cover and simmer slowly for 25 minutes or until tender. The onions should absorb most of the water. If there is water remaining after cooking, drain the excess. Set aside.
Prepare the mushrooms a few minutes before serving the stew. Sauté quartered mushrooms in a few tablespoons of butter and olive oil until browned and cooked through.
When the stew meat has cooked sufficiently, remove all solids from the sauce (except the beef) by draining through a colander set over a saucepan. Return the beef to the casserole. Press juices out of the residue into the cooking liquid, then remove any visible fat and boil down the liquid to 3 cups. Off heat, whisk in the beurre manié, then simmer for 2 minutes as the sauce thickens lightly. Correct seasoning and pour over the meat, folding in the onions and mushrooms. To serve, bring to a simmer, basting meat and vegetables with the sauce for several minutes until hot throughout.
Serve with rice, bread, or potatoes (unless you are doing the low-carb version!).