Brown the Beef: Slice the roast or boneless short ribs into large chunks. Choose the Instant Pot sauté setting and add the olive oil. When the oil is hot and shimmering, add the beef. Cook the beef, turning it often, until all sides are browned, about 10 minutes in total. 

Add Liquids and Seasonings: Pour off any excess drippings, then add the garlic, beef stock, bouillon, pepperoncini juice, Italian salad dressing mix, oregano, and basil. 

Pressure Cook: Ensure the lid is locked in place and set to sealing; then, select the pressure cook button. Set the timer for 60 minutes. When the time is up, let the pressure come down naturally for 15 to 20 minutes.

Shred the Beef: Remove the meat and shred it with 2 forks. 

Simmer the Juices: Place the juices in a gravy or fat separator and return them to the pot. Set the Instant Pot to simmer. Simmer for 1 to 2 minutes, until the mixture is hot.

Assemble the Sandwiches and Serve: Arrange the beef on toasted sub rolls and drizzle with 1 to 2 tablespoons of the juice. Top with pepperoncini peppers, giardiniera, and sliced provolone or mozzarella cheese. Place the sandwiches on a baking sheet and broil until the cheese is just melted. Put any extra jus in a bowl for dipping, if desired.