Cut roast into 2-3 large chunks.
Season roast pieces generously with salt and pepper. Turn Instant Pot to "saute" and drizzle of olive oil. Sear all sides of the roast pieces until slightly golden brown (1-2 minutes per side).
Using the flat part of a knife, strike your garlic clove quickly to smash it down into a patty-like shape. (You don't want to break the clove apart, rather expose the aromatic garlic flesh and oils to ensure more flavorful cooking.)
Pour the beef broth into pot, scraping up any brown bits from searing the roast. Add onion soup mix, Au Jus mix, Worcestershire sauce, and smashed garlic. Add roast pieces to Instant Pot.
Put the lid on your Instant Pot and seat. Cook on high pressure for 20 minutes per pound. Then do a natural release for 15 minutes once done cooking. If there is still pressure after 15 minutes, then do a quick release to remove the rest of the pressure.
While the Instant Pot is depressurizing, melt butter in a pan over medium high heat. Add onions and mushrooms. Cook, tossing frequently, until veggies are slightly caramelized.
Meanwhile, preheat oven to broil on high. Butter inside of rolls and toast under broiler for 5 minutes. Set aside once slightly toasted.
Pull roast out of Instant Pot and put onto a cutting board. Using two forks, shred the meat.
Strain the cooking liquid through a colander directly back into the pressure cooker. This will remove all the little pieces from the soup mix and fat particles to make a silky-smooth broth. Spoon ¼ cup of broth into a small dish for each diner.
Leave any remaining broth in the Instant Pot. Add shredded meat back to pot and toss meat in broth to coat.
Build your sandwiches by putting a heaping pile of shredded meat on one side of the bun. Add caramelized onions and mushrooms. Top with Swiss cheese and broil for 3 minutes, until cheese is melty. Cover with other side of bun.
Serve with individual bowls of broth dip.