In a large skillet with 1 T olive oil, lightly brown the bacon. Remove with a slotted spoon and set aside.
Blot the meat with paper towels. Add the meat in batches so as not to overcrowd the pan, and brown in the bacon fat on all sides. Remove meat to a Dutch oven or large covered casserole dish. Season the meat with salt and pepper.
Discard the bacon fat leaving ~1-2 T in the skillet. Add the onions and carrots to the skillet and brown lightly. Transfer to the pot with the meat. Deglaze the skillet with the red wine, scraping up the browned bits with a wooden spoon. Add the wine to the pot with the meat. Also add the tomatoes, bacon, and bouquet garni. Add enough beef stock so there's enough liquid to cover the meat. Put in the oven, covered, to simmer 2 hours.
Blanch the pearl onions 1 minute. Drain and rinse with cold water to stop the cooking. Cut off the end tips, remove the skins, and score an "x" in the root end. Heat a skillet with 1-2 T butter. Lightly brown the onions. Add enough chicken stock to half submerge the onions. Simmer gently 25 minutes or until tender.
When meat is almost done cooking, prepare the mushrooms. Heat 2 T butter in a large skillet. Add the mushrooms and cook until browned. Mine soaked the butter right up and looked a little dry, so I added a ~1T olive oil for them to cook properly. Once browned, remove the mushrooms from the heat and set aside.
Remove the Dutch oven from the oven. Using thongs, pick out the meat onto a dish. Strain the remaining liquids and such from the Dutch oven into a large saucepan. Discard the onions, carrot, and bouquet garni. Return the meat to the Dutch oven. Skim off as much fat as possible from the juices in the saucepan. Simmer liquid down to ~2 1/2 c (I didn't do this enough, so my sauce was a little thin). Remove from the heat, whisk in the beurre manié, return to the heat, and simmer 2 minutes. Pour over the meat. Add the pearl onions and mushrooms. Serve over the starch of your choice which is traditionally roast potatoes - I made my Cream Cheese Smashed Potatoes.
Julia boiled her bacon a couple minutes first to get the smoky flavor out. I didn't.