Cut the beef chuck roast into 4 to 6 pieces, trimming excess fat and pat dry with paper towels.
Mix all the seasoning mix ingredients in a bowl and thoroughly coat the beef pieces with the seasoning.
Turn on the Instant Pot to SAUTÉ and set to MORE, wait until it displays HOT.
Pour 2 tablespoons olive oil into the pot, add half the seasoned beef, and sear each side for 2 to 3 minutes until browned. Remove to a plate.
Repeat searing with the remaining 1 tablespoon olive oil and beef pieces, then set all beef aside.
Cancel SAUTÉ mode and start it again on REGULAR. Add diced onions and minced garlic, cooking for 2 to 3 minutes until softened.
Stir in tomato paste, cooking while scraping the pot bottom to lift browned bits.
Pour in the red wine, beef broth, and Worcestershire sauce.
Nestle the seared beef chunks into the liquid, then arrange the carrots and potatoes on top without stirring.
Seal the Instant Pot lid, set to MANUAL at HIGH pressure for 35 minutes, ensuring the steam valve is in SEALING position.
After cooking completes, allow a natural pressure release for 10 minutes, then quick-release any remaining steam before opening.
Remove carrots and potatoes to a serving dish and cover with foil to keep warm.
Transfer beef to a cutting board and let it rest while preparing the gravy.
Set Instant Pot to SAUTÉ on LOW, stir ½ cup water into the remaining cooking liquid and adjust dilution to taste.
In a separate bowl, mix 2 tablespoons cold water with cornstarch to form a slurry.
Whisk the slurry into the pot, simmer for about 5 minutes until the gravy thickens, stirring occasionally.
Cancel the Instant Pot and unplug it, then pour gravy into a gravy boat.
Serve shredded or chunked pot roast alongside carrots, potatoes, and plenty of the savory gravy.