In a small bowl, mix all the rub ingredients.
Season the brisket all over with the rub. If you have time, let it sit in the refrigerator wrapped in plastic for up to 24 hours.
In a medium bowl, mix all the BBQ sauce ingredients.
Turn the instant pot/pressure cooker to "saute". Add the oil and allow it to get hot. Add the brisket to the pot and sear both sides for about 4-5 minutes or until golden brown. Remove the brisket from the pot and place it in a bowl or plate. Add the garlic and cook for about 1 minute, making sure the garlic doesn't burn.
Press the keep warm/cancel button on the instant pot. Add the broth and with a wooden spoon or spatula scrape the bottom of the pot to remove some of the bits stuck at the bottom of the pot. Add the BBQ sauce. Return the brisket to the pot with any collected juices. Toss well making sure the meat is well coated. Close the lid. Set the instant pot to meat/stew and set the timer to 75 minutes. *See Chef's Tips
Once the cooking cycle is complete, allow the pressure to release naturally for about 10 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.