Pat the beef chuck dry with paper towels and season 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 deeply browned on all sides.
Add the sliced carrots and cremini mushrooms to the pot, sautéing for 4-5 minutes until the vegetables begin to soften and brown.
Stir in the minced garlic and tomato paste, cooking for 1 minute until the paste turns a dark brick red and smells fragrant.
Pour in the red wine to deglaze the pot, using a wooden spoon to scrape up all the flavorful browned bits from the bottom.
Add the beef broth, thyme sprig, and bay leaf, then bring the liquid to a gentle boil.
Reduce the heat to low, cover the pot tightly, and simmer for 60 to 90 minutes until the beef is fork-tender.
Stir in the pearl onions during the final 15 minutes of simmering to allow them to soften without losing their shape.
Remove the bay leaf and thyme sprig before serving the stew in a warm bowl.