Trim any excess fat from the beef chuck 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 hot oil until a deep brown crust forms on all sides, then remove the meat and set aside.
In the same pot, add the mushrooms, sliced carrots, and pearl onions, sautéing for 5-7 minutes until the vegetables begin to soften and brown.
Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant.
Pour in the red wine to deglaze the pan, using a wooden spoon to scrape up all the flavorful browned bits from the bottom.
Return the beef to the pot and add the beef broth, thyme sprig, and bay leaf.
Bring the liquid to a gentle simmer, then cover with a tight-fitting lid and reduce heat to low.
Braise for 90 minutes, or until the beef is fork-tender and the sauce has thickened into a rich glaze.
Remove the bay leaf and thyme sprig before serving hot.