Rub the roast with olive oil and generously season with salt and pepper. Preheat your air fryer to 400°F (200°C) and sear the roast for 20-25 minutes, flipping halfway through.
While the roast sears, peel and chop the carrots and potatoes into chunks. Dice the onion and mince the garlic.
Once seared, transfer the roast to a baking dish that fits inside the air fryer. Surround the roast with the prepared carrots, potatoes, onion, and garlic.
Pour the beef broth and red wine over the roast, then sprinkle with thyme, rosemary, and add the bay leaves.
Reduce the air fryer temperature to 320°F (160°C), place the dish in the air fryer basket, and cook for 1.5 to 2 hours, checking occasionally. Add more broth or water as needed to keep the dish moist.
Once the roast is tender and shreds easily with a fork, remove it from the air fryer and let it rest for 10 minutes. Slice the roast and serve with the vegetables, drizzling the flavorful broth over the top.