Trim any excess fat from the chuck roast to prevent the dish from becoming greasy. Pat the roast dry with paper towels, then season generously with salt and black pepper on all sides.
Set your Instant Pot to the sauté function and heat the vegetable or olive oil. Once hot, add the roast and brown it on all sides, about 4-5 minutes per side. Remove the roast and set it aside.
Add the diced yellow onion to the pot and sauté until softened and fragrant, about 3-4 minutes. Use a wooden spoon to scrape up any browned bits stuck to the bottom of the pot.
Pour in the beef broth, then stir in the tomato paste and Worcestershire sauce until well combined. Add the dried rosemary, dried thyme, and bay leaves. Mix everything together.
Place the browned chuck roast back into the Instant Pot, nestling it into the broth mixture. Lock the lid in place and set the valve to sealing. Cook on high pressure for 60 minutes.
When the cooking time is complete, carefully perform a quick release to release the steam. Open the lid and add the halved baby potatoes and thick carrot chunks around the roast.
Close the lid again, set the valve to sealing, and cook on high pressure for an additional 10 minutes. Once done, perform another quick release.
Remove the bay leaves and discard. Slice or shred the pot roast and serve hot with the tender carrots and potatoes, spooning the rich broth over the top.