Cut the boneless beef chuck roast in half to help it brown more evenly and fit in the Instant Pot. Sprinkle kosher salt and ground black pepper on all sides of the beef, ensuring it is well-seasoned before cooking.
Heat the olive oil in the Instant Pot set to sauté mode until it is hot. Place the seasoned beef in the pot and brown it on both sides, about 4 minutes per side. Avoid moving the beef until you are ready to turn it, allowing a good sear to develop. Once both sides are browned, transfer the beef to a clean plate.
With the Instant Pot still on sauté mode, add the chopped onion to the pot. Cook until the onion is softened and lightly browned, stirring often and scraping up the browned bits from the bottom, about 4 minutes. Add the minced garlic, stir, and then press Cancel to turn off the sauté function.
Stir in the tomato paste, Worcestershire sauce, and beef broth, ensuring you scrape up any remaining browned bits for maximum flavor. Return the browned beef (from Step 2) to the Instant Pot, then add the fresh thyme sprigs or dried thyme on top. Secure the lid and set the steam release valve to sealing. Cook on Manual/Pressure Cook, high pressure, for 60 minutes. When the cooking time finishes, let the pressure release naturally for 10 minutes, then quickly release any remaining pressure.
Open the Instant Pot and layer the carrot chunks and baby potatoes on top of the beef. Close the lid, set the valve to sealing, and cook on high pressure for 5 minutes. Allow the pressure to release naturally for 10 minutes before quick releasing any remaining pressure. This step ensures the vegetables become tender but not overcooked. I always wait for the natural release for better texture in the vegetables.
Remove the beef and vegetables from the Instant Pot, leaving the juices behind. Discard thyme stems if you used whole sprigs. Use two forks to shred the roast into generous chunks. To thicken the sauce (optional), turn the Instant Pot back to sauté mode, mix cornstarch and water in a small bowl, and pour into the juices. Cook, stirring occasionally, until the gravy thickens slightly. I like to let the gravy simmer for an extra minute for a richer texture.
Serve the shredded pot roast with carrots, potatoes, and a generous spoonful of thickened gravy. Enjoy this comforting meal hot.