Pat the beef chuck dry with a paper towel and season all sides 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 in the pot until a deep golden-brown crust forms on all sides, then remove the meat and set aside.
In the same pot, add the sliced mushrooms, carrots, and pearl onions, sautéing for 5 minutes until the vegetables begin to soften.
Stir in the minced garlic and tomato paste, cooking for 1 minute until the paste turns a deep brick red.
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 bone broth, thyme sprig, and rosemary sprig.
Bring the liquid to a gentle boil, then reduce the heat to low and cover with a tight-fitting lid.
Simmer for 60 to 75 minutes, or until the beef is fork-tender and the sauce has reduced into a thick glaze.
Remove the herb sprigs and serve the stew warm in a shallow bowl.