Pat the beef chuck dry with paper towels and season thoroughly 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 a deep golden crust forms on all sides.
Remove the beef from the pot and set aside, then add the pearl onions, sliced carrots, and halved mushrooms to the same pot.
Sauté the vegetables for 5 minutes until they begin to soften, then stir in the minced garlic and tomato paste 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 seared beef to the pot along with the beef bone broth, thyme sprig, and bay leaf.
Lower the heat to a gentle simmer, cover tightly, and cook for 60 to 90 minutes until the beef is tender and the sauce has reduced to a thick glaze.
Discard the thyme sprig and bay leaf before serving the stew in a shallow bowl.