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.
Sear the beef cubes in the pot until a deep brown crust forms on all sides, then remove the meat and set it aside on a plate.
In the same pot, add the pearl onions, sliced carrots, and halved mushrooms, sautéing for about 5 minutes until the vegetables begin to brown.
Stir in the minced garlic and tomato paste, cooking for 1 minute until the paste turns a deep brick red.
Pour in the dry red wine to deglaze the pot, using a wooden spoon to scrape up all the flavorful browned bits from the bottom.
Return the seared beef and any accumulated juices to the pot, then add the beef bone broth and the fresh thyme sprig.
Bring the liquid to a gentle boil, then reduce the heat to low, cover with a tight-fitting lid, and simmer for 60 to 90 minutes until the beef is fork-tender and the sauce has thickened into a rich glaze.