Pat the roast halves dry and season all over with the salt and pepper.
Set the Instant Pot to Sauté. Once it's hot, add the olive oil and sear the roast halves on all sides until browned. Move them to a plate.
Add the onion to the oil left in the pot and cook for 3 to 4 minutes, until softened and starting to brown. Stir in the garlic, then press Cancel to turn off the Instant Pot.
Add the beef broth, Worcestershire sauce, and tomato paste. Stir well, scraping up any browned bits from the bottom.
Set the roast halves back in the pot on top of the broth mixture. Lay one thyme sprig on each half and drop the third sprig into the broth.
Lock the lid and turn the valve to Sealing. Cook on high pressure for 60 minutes. Let the pressure release naturally for 5 minutes, then turn the valve to Venting to release the rest.
Add the carrots and potatoes and stir gently so they're coated in the broth.
Lock the lid again and turn the valve to Sealing. Cook on high pressure for 10 minutes. Let the pressure release naturally for 10 minutes, then release the rest.
Move the roast to a cutting board and shred it with two forks. Remove the thyme stems. Either stir the shredded beef back into the pot with the vegetables, or serve the beef on a platter with the carrots and potatoes alongside and the broth spooned over the top.