Pat the beef chuck roast dry with paper towels and season all sides evenly with sea salt and black pepper.
Heat the olive oil in a small Dutch oven or heavy-bottomed pot over medium-high heat.
Sear the beef for 3-4 minutes per side until a deep brown crust forms, then remove the meat and set aside on a plate.
Reduce heat to medium and add the diced onion, carrots, and celery to the pot, sautéing for 5 minutes until the vegetables soften and begin to brown.
Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant and the paste turns a dark brick red.
Pour in the red wine, using a wooden spoon to scrape up all the flavorful browned bits from the bottom of the pot.
Return the beef to the pot along with any accumulated juices, then pour in the beef broth and add the fresh thyme sprigs.
Bring the liquid to a gentle simmer, then cover with a tight-fitting lid and reduce heat to low.
Cook for 2.5 to 3 hours, or until the beef is tender and easily pulls apart with a fork.
Remove the thyme sprigs and serve the beef with the braising liquid and vegetables spooned over the top.