Trim excess fat from the beef chuck and cut into one-inch cubes, then pat dry with paper towels and season with sea salt and black pepper.
Heat the ghee in a heavy-bottomed pot or Dutch oven over medium-high heat.
Sear the beef in batches until a deep brown crust forms on all sides, then remove the meat and set it aside.
Add the pearl onions, sliced carrots, and halved mushrooms to the pot, sautéing for five minutes until the onions become translucent and golden.
Stir in the minced garlic and tomato paste, cooking for one minute until the paste turns a dark brick red and smells fragrant.
Pour in the red wine to deglaze the pot, using a wooden spoon to scrape up the flavorful browned bits from the bottom.
Return the beef to the pot along with the beef broth, fresh thyme sprig, and bay leaf.
Bring the liquid to a gentle simmer, then cover and reduce heat to low, cooking for 90 minutes until the beef is fork-tender.
Discard the thyme sprig and bay leaf before serving the hot stew in warm bowls.