Trim the beef chuck of excess fat and cut into 1-inch cubes, then season evenly with sea salt and black pepper.
Heat the olive oil in a heavy-bottomed pot or Dutch oven over medium-high heat and sear the beef until browned on all sides.
Remove the beef from the pot and add the pearl onions, sliced carrots, and halved mushrooms, sautéing for 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant and the paste darkens slightly.
Pour in the dry red wine to deglaze the pan, using a wooden spoon to scrape up any browned bits from the bottom.
Return the beef to the pot and add the beef bone broth, thyme sprig, and bay leaf.
Bring the liquid to a gentle simmer, then cover and reduce heat to low, cooking for 60 to 90 minutes until the beef is fork-tender and the sauce has thickened.
Remove the bay leaf and thyme sprig before serving warm.