Trim any excess fat from roast. Season roast with salt and pepper.
Pour oil into your Instant Pot and set to the high sauté function. When the oil is heated, sear roast on all sides until browned (using tongs to turn). *If your roast is too large, you may need to cut it in half (across the grain) and sear in 2 batches, adding more olive oil as necessary.* Transfer roast to a plate.
Pour in 1 cup of the beef broth to deglaze the pot. Using a wooden spoon, stir to scrape the bottom of the pot to remove browned bits. Add the remaining beef broth, soup, cola, soy sauce, garlic powder, bay leaves, thyme, and oregano. Stir to combine. Turn off the sauté function.
Return roast to the pot. Place the lid on your pressure cooker and lock. Steam release knob should be set on "sealing". Cook on manual setting (high pressure) for 90 minutes.
Allow the pressure to release naturally for 20 minutes, then quick release the remaining pressure. Remove and discard bay leaves.
Carefully remove the roast and transfer to a cutting board or large platter. Shred roast or slice across the grain.
Preheat your oven to 375 degrees F. Slice buns and place on a rimmed baking sheet. Place beef on top of buns and top each with 2 slices of provolone cheese. Bake until the cheese is melted (about 3 to 4 minutes).
Sprinkle with chopped fresh parsley when serving, if desired. Serve with au jus from the Instant Pot.