Set the Instant Pot to Sauté, add a little oil, and cook the diced onion and minced garlic until softened, then stir in 1 tbsp tomato paste and cook for 1 minute. The onion should look glossy and the tomato paste should darken slightly and smell richer.

Add the beef chunks to the pot with the oregano, basil, onion powder, paprika, garlic powder, red pepper flakes, salt, and black pepper. The seasoning should coat the meat and the pot should smell savory with a little whiff of garlic and herbs.

Pour in the beef broth, 1 tsp Worcestershire sauce, and the giardiniera brine if using, then make sure nothing is stuck to the bottom before sealing the lid. The liquid should loosen any browned bits so the bottom of the pot looks clean rather than scorched.

Cook on high pressure for about 60 minutes, then let the pressure release naturally for 10 to 20 minutes before opening the lid. When you open the pot, the beef should look deeply browned and smell rich, tangy, and beefy.

Transfer the beef to a board or bowl and shred it with two forks, then return it to the juices if you want it extra moist. The meat should pull apart easily without resistance.

Place a slice of provolone on each side of the rolls and broil until melted, then fill the rolls with beef and top with giardiniera. The cheese should be melty and the roll edges lightly toasted.

Serve the sandwiches hot with some of the cooking liquid on the side for dipping. The best bites are juicy and messy, so napkins are a very good idea.