In a large covered ovenproof casserole dish or sauté pan, sauté the bacon over moderate heat for 2 to 3 minutes until lightly browned. Remove bacon with a slotted spoon, reserving the grease, and drain on paper towels. Set aside. Reheat bacon fat until almost smoking.
Dry the meat with paper towels to ensure that it will brown properly. Brown meat in oil in batches. Remove the meat with a slotted spoon, reserving the bacon grease, and set aside with the bacon.
Sauté the carrots, sliced onion, and garlic for 3-5 minutes or until lightly browned. Add the black pepper and flour and continue to sauté, stirring frequently, to remove the raw flour flavor, about 2-3 minutes more.
Add the wine and the broth, scraping up any browned bits on the bottom of the pan. Stir in the tomato paste, thyme, and bay leaf. Return the beef and bacon to the casserole dish or sauté pan and toss with vegetables.
Preheat oven to 325 degrees. Cover casserole dish and place in the bottom third of the oven. Braise for 2-1/2 to 3 hours or until the meat pierces easily with a fork.
Alternately, add everything to the crock of a slow cooker. Cook on low for 6-8 hours.
Forty-five minutes before serving, sauté the mushrooms and onion in butter for 3-5 minutes. Add to the casserole or crock pot and continue cooking.
Serve stew over mashed potatoes or egg noodles.