Prep and preheat. Preheat oven to 325°F (165°C). Pat the beef dry with paper towels and season with about 1 teaspoon salt and ½ teaspoon pepper.
Cook the bacon. Add the bacon to a large Dutch oven and cook over medium heat until the fat renders and the bacon is crisp, 4-5 minutes. Transfer bacon to a bowl with a slotted spoon, leaving the fat in the pot. Add a bit of oil if there is less than a couple tablespoons of fat.
Brown the beef. Increase heat to medium-high. Working in batches, brown the beef in a single layer, turning to deeply brown at least two sides, 3-4 minutes per side. Don’t crowd the pan. Transfer browned beef to the bowl with the bacon and repeat with remaining beef, adding a touch of oil as needed.
Sauté the vegetables. Reduce heat to medium. Add the onion and carrots to the pot. Cook, stirring occasionally, until the onion softens and begins to brown, about 5-7 minutes. Stir in the garlic and cook about 30 seconds, just until fragrant.
Add tomato paste and flour. Stir in the tomato paste and cook 2-3 minutes, stirring, until it darkens slightly in color. Sprinkle the flour over the vegetables and stir to coat. Cook 1-2 minutes to remove the raw flour taste.
Deglaze with wine. Slowly pour in the red wine while stirring and scraping the bottom of the pot to release any browned bits. Bring to a simmer and let it bubble for 2-3 minutes to start reducing.
Build the braise. Stir in the beef stock, bay leaf, and thyme. Return the browned beef and bacon (along with any juices) to the pot and stir. The liquid should just about cover the meat - add a bit more stock or wine if needed. Taste the liquid and lightly season with salt and pepper, keeping in mind it will reduce.
Oven braise. Bring the pot to a gentle simmer on the stovetop. Cover with a tight-fitting lid and transfer to the oven. Braise for about 2½ hours, stirring once halfway through, until the beef is mostly tender but not yet falling apart.
Cook mushrooms and pearl onions. About 30-40 minutes before the 2½-hour mark, heat the butter in a large skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until they release their moisture and turn golden brown, 4-5 minutes. Add the pearl onions and cook until lightly caramelized and just tender, 5-8 minutes. Season with a pinch of salt and pepper and set aside.
Finish the stew. After about 2½ hours, check the beef. When it’s nearly fork-tender, stir in the sautéed mushrooms and pearl onions. Return the pot to the oven, uncovered, for another 30-45 minutes, until the beef is very tender and the sauce is glossy and slightly thickened (it should coat the back of a spoon).
Adjust and serve. Remove the bay leaf and thyme stems. If there is excess fat on top, skim it off. If the sauce is too thin, simmer gently on the stovetop to reduce. If it’s too thick, loosen with a splash of stock or wine. Taste and adjust with more salt and pepper. Let rest 10-15 minutes, then garnish with parsley if desired and serve.