Cook the bacon: Preheat the oven to 350°F. Place a Dutch oven over medium heat, add the bacon, and cook until the fat renders. Remove the bacon with a slotted spoon and set aside.
Sear the beef: Pat the beef cubes dry with paper towels, then season generously with salt and pepper. Lightly dust with flour. Increase the heat to medium-high and sear the beef in batches until browned on all sides, about 2–3 minutes per side. Set aside with the bacon.
Sauté the vegetables: In the same pot, add the carrots and onions. Cook for about 5 minutes, until softened. Stir in the garlic and cook for another minute, then add the tomato paste and cook for one more minute.
Deglaze with Cognac: Turn off the heat if using a gas stove. Carefully pour in the Cognac and ignite with a long lighter or match to burn off the alcohol (optional, but fun!). Once the flame subsides, scrape up the browned bits from the bottom of the pot.
Add the liquids and herbs: Return the beef and bacon to the pot. Pour in the wine and enough beef stock to just cover the meat. Add the thyme and bay leaves, season with salt and pepper, and bring to a gentle simmer.
Braise in the oven: Cover and transfer the pot to the oven. Lower the temperature to 325°F and cook for 2½–3 hours, until the beef is fork-tender and the sauce has reduced by about a quarter.
Prepare the mushrooms and onions: While the stew cooks, heat butter and olive oil in a skillet over medium heat. Add the mushrooms and cook until browned and their moisture evaporates, about 10 minutes. Add the pearl onions, wine, thyme, bay leaf and a pinch of salt and pepper. Simmer until the wine has reduced and the onions are tender.
Combine and serve: When the beef is done, remove the bay leaves and thyme stems. Skim any excess fat from the top if needed. Stir in the mushroom and onion mixture, sprinkle with fresh parsley, and serve.