Preheat your oven to 325°F (160°C). Pat the beef cubes dry with paper towels and season generously with salt and pepper.
In a large Dutch oven over medium heat, cook the diced bacon until crisp and the fat renders, about 8 minutes. Remove bacon with a slotted spoon and set aside, leaving the fat in the pot.
Increase heat to medium-high. Working in batches, add beef cubes to the hot bacon fat and sear until deeply browned on all sides, about 3-4 minutes per batch. Transfer browned beef to a plate.
Lower heat to medium. Add pearl onions and carrots to the pot and cook for 5 minutes until onions start to soften. Stir in garlic and tomato paste, cook for 1 minute more.
Sprinkle flour over vegetables and stir for 1 minute. Pour in the red wine and beef stock, scraping up any browned bits from the bottom. Return beef and bacon (reserve some for garnish if desired) to the pot. Add thyme and bay leaves. Bring to a simmer.
Cover the pot with a lid and transfer to the preheated oven. Braise for 2 to 2½ hours, or until the beef is fork-tender and reaches an internal temperature of at least 145°F (63°C).
While the stew cooks, heat a skillet with olive oil over high heat. Sauté the quartered mushrooms with a pinch of salt until golden and moisture evaporates, about 6-8 minutes. Set aside.
Remove the Dutch oven from the oven. Discard thyme sprigs and bay leaves. Stir in the sautéed mushrooms and simmer on the stovetop for 5 minutes. Taste and adjust seasoning.
Ladle the beef bourguignon into bowls, top with reserved crispy bacon and fresh parsley. Serve immediately with crusty bread or egg noodles.