Set the Instant Pot to Sauté mode and allow it to preheat. Add the rub ingredients to a small bowl and stir to combine.
Trim the brisket to roughly the size of your Instant Pot. It will shrink during the cook, so it can be slightly larger. Trim the fat cap of the brisket to around ¼ inch thick and remove any large pockets of fat and thin edges of the meat. Then season the brisket liberally on all sides with the rub.
Add the olive oil to the Instant Pot, then place the meat in the pot and sear for 2-3 minutes on each side until well browned. Transfer the meat to a plate and cancel the Sauté mode.
Add the beef broth and thoroughly scrape the pot with a wooden spatula or spoon to remove any brown bits. Add the BBQ sauce to the pot and stir to combine.
Add the brisket back to the pot and any juices from the plate. Lock the lid and cook on high pressure for 75 minutes. Let the pressure release naturally for 15 minutes, then vent any remaining pressure.
Using a pair of tongs, remove the brisket from the pot and transfer it to a cutting board. Tent it with foil and let it rest for 10 minutes. Slice the brisket across the grain into thin slices and top with some of the juices from the pot before serving.
Notes
To cook a larger piece of brisket, you can cut the meat in half and place the pieces in the pot side-by-side.Store your leftovers in an airtight container with some of the cooking liquids and refrigerate for up to 4 days.To reheat leftovers, place them in a baking dish with some of the cooking liquids and cover with foil. Heat in a 275°F oven for 10 minutes or until warmed through.