Preheat your oven to 300°F (150°C).
Pat the chuck roast dry and season generously with kosher salt and black pepper.
Heat olive oil over medium-high heat and sear the roast for about 5 minutes on each side until browned. Remove and set aside.
Reduce heat to medium, add butter, and cook sliced onions for 25–30 minutes until caramelized. Add beef broth if needed.
Stir in minced garlic, cook for 2 minutes, then add apple cider vinegar, scraping browned bits from the pot.
Sprinkle flour over onions, stirring well, then gradually add beef broth and Worcestershire sauce until smooth.
Add bay leaves, rosemary, and thyme. Bring to a gentle simmer.
Nestle the seared chuck roast into the onion mixture, adding enough broth to cover ¾ of the meat.
Cover the pot tightly and braise in the oven for 3½ hours or until fork-tender.
Remove bay leaves and herbs. Shred beef into large chunks in the sauce.
Increase oven temperature to 400°F (200°C). Sprinkle shredded cheese over beef and bake uncovered for 5–7 minutes until melted.
Serve warm over mashed potatoes or with toasted baguette slices.