Cut the chuck roast into 4 to 6 chunks, separating at the seams to expose the fat deposits (if using a highly marbled chuck roast). Use a sharp knife to trim as much of the fat as possible from the chunks of roast. It's fine if some fat remains but trim as much as you can to ensure that your gravy will not be overly greasy. Place the trimmed chunks of roast on a large piece of foil for easy cleanup.
Combine the spice rub ingredients in a small bowl. Sprinkle the rub over the pieces of beef and use your hands to press the seasoning into the meat. Wash those hands!
Press the SAUTÉ key on the instant pot and the ADJUST key to toggle to the MORE setting. Wait for the pot to say "HOT" before adding ingredients.
Add 2 tablespoons olive oil to the heated pot. Add half of the seasoned beef (or as much as will fit comfortably without being too crowded) and sauté for 2 to 3 minutes per side, or until nicely seared. Transfer seared beef to a plate and repeat with remaining 1 tablespoon oil and the rest of the beef. Transfer second batch of beef to the plate and set aside.
Press CANCEL and then select SAUTÉ again and ADJUST to the REGULAR setting. Add the onions and garlic to the pot and sauté for 2 to 3 minutes or until tender. Add the tomato paste and cook, stirring to scrape up any browned bits from the bottom. Add the red wine, broth, and Worcestershire sauce. Nestle the chunks of browned beef down into the sauce and then top with the carrots and potatoes. Don't stir. You want the meat submerged in liquid and the carrots and potatoes on top.
Place the lid on the Instant Pot. Press the MANUAL button, select HIGH, and set the time to 35 minutes (making sure the steam release handle is in the "Sealing" position). After the cooking is complete allow the Instant Pot to do a natural release for 10 minutes then use a long handled spoon to push the steam release handle to the "Venting" position to allow any remaining steam to release completely before you open the pot. Press CANCEL.
Transfer the carrots and potatoes to a serving dish and tent with foil to keep warm. Transfer the beef to a cutting board and let it rest while you make the gravy.
Press SAUTÉ and ADJUST to select the LOW setting Stir 1 cup water into the very concentrated cooking liquid in the Instant Pot to dilute it a bit. Taste and if needed, add additional 1/2 cup of water to dilute as desired. In a small bowl stir together 2 tablespoons water and 2 tablespoons cornstarch. Whisk the mixture into the Instant Pot and simmer for about 5 minutes or until the gravy has thickened to your liking, stirring occasionally. Press CANCEL and unplug the Instant Pot. Transfer the gravy to a gravy boat.
Shred or chunk the roast and serve with the potatoes, carrots, and plenty of gravy!