Begin heating the Instant Pot (or another electric pressure cooker) using the sauté function. Add the oil and swirl with a turner spatula to cover the bottom of the pan, heating just until the oil shimmers. Add the roast and sear the meat on each side when the oil is hot (but not smoking!). Be careful as the oil may spatter a bit. Using a splatter guard is an excellent idea if you have one on hand.
When the roast’s sides are nicely browned, remove the roast from the cooker and set it aside. Add the beef broth and pickle juice to the pot, bringing to a simmer as you deglaze the pot, scraping up all the tasty brown bits. Once the pan is deglazed, turn off the sauté function.
Return the meat to the pressure cooker. Sprinkle the roast with garlic powder, dried onions, and freshly ground black pepper. Using the pressure cook function, set the cooker to high pressure for one hour for a boneless roast or 1 hour and 15 minutes for a bone-in roast.
When the time is done, let the pressure release naturally for 10 minutes, and then press the release button to complete the pressure release. Remove the roast from the Instant Pot, and reserve the cooking liquid in a separate container. As soon as the meat is cool enough to handle, use two forks to shred the meat, removing any extra fat. Return the beef to the pot and set the Instant Pot to the keep warm function.
Meanwhile, while the roast is cooking, stir together the ingredients for the barbecue sauce. Once the meat is shredded, mix the sauce into the meat. Add some cooking liquid back in, a little at a time, until the meat reaches the juiciness you prefer.
Keep the BBQ beef warm in the cooker until ready to serve.
Serve shredded BBQ beef piled high on a toasted hamburger bun spread with mayonnaise, sliced dill pickles, and a slice of cheese. Add a handful of potato chips to your plate and a side of coleslaw for a complete All-American summertime meal!