Cut the chuck roast into 4 to 6 pieces, trimming away excess fat while keeping some for flavor, then pat the pieces dry with paper towels.
Mix all the seasoning mix ingredients together and rub evenly onto the beef chunks, pressing firmly to adhere.
Set the Instant Pot to SAUTÉ mode, select MORE for higher heat, and wait for it to heat up until HOT shows.
Pour in 2 tablespoons of olive oil, add half the seasoned beef pieces without crowding, and sear each side for 2 to 3 minutes until browned; remove and set aside.
Repeat the searing process with remaining 1 tablespoon olive oil and beef pieces, then turn off SAUTÉ mode.
Add diced onions and minced garlic to the pot and cook on SAUTÉ regular setting for about 2 to 3 minutes until softened.
Stir in tomato paste and cook while scraping browned bits off the bottom, then add red wine, beef broth, and Worcestershire sauce.
Nestle the seared beef pieces into the liquid, place carrots and baby potatoes on top without stirring to keep beef submerged.
Secure the lid and seal the steam release. Set the Instant Pot to MANUAL on HIGH pressure for 35 minutes.
After cooking, allow a natural pressure release for 10 minutes, then carefully release remaining steam before opening.
Remove carrots and potatoes to a warm dish, and transfer beef to a cutting board to rest.
Select SAUTÉ mode again and switch to LOW heat; add ½ cup water to the cooking liquid to dilute if needed.
Whisk together cold water and cornstarch to make a slurry and stir into the pot; simmer for about 5 minutes until gravy thickens, stirring occasionally.
Turn off the Instant Pot and pour the gravy into a serving container.
Serve the shredded or chunked beef with the tender carrots, potatoes, and generous gravy.