Trim any excess fat and if needed, cut the meat into smaller pieces so they fit comfortably in your pressure cooker. Pat the meat dry with paper towel to get a nice sear.
In a small bowl, mix all the rub ingredients, then rub the spice mix all over the meat. At this point, you can cook the brisket or wrap it with plastic wrap and store it in the refrigerator for up to 24 hours.
In a medium bowl, mix all the barbecue sauce ingredients.
Turn the instant pot to sauté mode and add the olive oil. When hot, sear the meat on both sides for about 3-5 minutes per side or until golden brown. If you have cut the brisket in smaller pieces, do this in batches not to overcrowd the pot.
Transfer the meat to a plate. If your instant pot is too hot, turn the sauté function off to prevent burning the garlic. Stir in garlic and sauté for 30 seconds to a minute.
If you haven't done so already, hit the warm/cancel button. Add the broth and with a wooden spoon or spatula scrape the bottom of the pot to remove the browned bit that are stuck at the bottom of the pot. Add the BBQ sauce.
Return the brisket to the pot with any collected juices. Close the lid and set the pot to manual and the timer to 75 minutes.
Once the cooking cycle is complete, allow the pressure to release naturally for about 10-15 minutes. Then do a quick release for the remaining pressure.
Transfer the brisket to a cutting board. Cover with aluminum foil and let the meat rest for about 10 -15 minutes.
Turn the instant pot/pressure cooker to "saute" and cook/reduce the sauce for 5 to 8 minutes, stirring a few times. Press the warm/cancel button.
Slice the beef brisket against the grain and serve with the BBQ sauce. You can also return the sliced brisket to the instant pot making sure the slices are covered with the sauce (to prevent the meat from drying). Keep it warm until ready to serve.