Pat the beef stew meat dry with a paper towel and 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 in the pot until a golden-brown crust forms on all sides, then remove the meat and set it aside.
In the same pot, add the halved mushrooms, sliced carrots, and diced onions, sautéing for 5-7 minutes until the onions are translucent.
Stir in the minced garlic and tomato paste, cooking for 1 minute until fragrant.
Pour in the dry red wine to deglaze the pot, using a wooden spoon to scrape up the flavorful browned bits from the bottom.
Return the seared beef to the pot and pour in the beef bone broth until the meat is mostly submerged.
Tuck in the fresh thyme and rosemary sprigs, bring to a gentle boil, then reduce heat to low.
Cover and simmer for 60 to 90 minutes, or until the beef is fork-tender.
In a small bowl, whisk the arrowroot powder with a teaspoon of water to create a slurry, then stir it into the stew and simmer for 2 more minutes to thicken the sauce before serving.