Preheat the oven to 450 degrees. Cut the rind off the bacon, reserving the rind. Slice the bacon meat into strips. Bring 6–8 cups of water to a boil; add the rind and the bacon meat, and simmer for 10 minutes. Drain, discard the liquid and rind, and pat the bacon meat dry.
In a large saucepan, warm the olive oil on medium heat. Sauté the bacon meat for 2 minutes to brown it slightly. With a fork, remove the bacon from pan and set it aside.
Cut the beef into 2-inch cubes and pat them dry with paper towels. Heat the bacon drippings on medium and sauté the beef, turning it several times to brown it on all sides. Remove the beef and set it aside with the bacon.
Slice the onion and carrot. Add them to the same oil to sauté for 4 minutes. Discard the oil, leaving the vegetables in the pan.
Using a large stove top- and ovenproof container with a lid, place the bacon and beef in the bottom. Sprinkle on salt, pepper, and the flour, rubbing them into the meats. Without its lid, place the dish in the oven for 4 minutes. Remove, toss the meats slightly and cook for 4 more minutes. Take out of the oven. Reduce oven temperature to 325 degrees.
Pour the wine and 2 cups of the broth over the meats. Mash the garlic and add it to the mixture, along with the tomato paste and herbs. Place the dish on the top of the stove, bringing it to a boil. Reduce to a simmer. Put the lid on the dish and place it back in the oven for 2½ hours, making sure it simmers very gently.
Meanwhile, heat the remaining broth in a saucepan. Simmer the pearl onions gently for 5 minutes. Quarter the mushrooms and add them, cooking the mixture for another 7 minutes. When the meat is ready, strain the casserole and discard most of the liquid, leaving just enough to create the thickness of soup. Skim off any fat. Place the onions and mushrooms on top, rewarm in the oven for 5 minutes, and serve. Discard the bay leaf.
This is as classic a French dish as bouillabaisse. Considered a stew, it can easily incorporate a bit more liquid and become a soup.