Trim any excess fat from the chicken breasts or thighs. Season them generously with salt, pepper, garlic powder, and onion powder.
Set the Instant Pot to "Sauté" mode. Once it's hot, add the olive oil. Place the seasoned chicken pieces in the pot and brown them for 2-3 minutes on each side. This adds flavor and helps to lock in juices.
Pour in the chicken broth or water and use a wooden spoon to scrape up any browned bits from the bottom of the pot. This prevents the Instant Pot from giving a burn notice.
Pour the BBQ sauce, Worcestershire sauce, and honey over the chicken. Stir to coat the chicken evenly with the sauce.
Close the Instant Pot lid and set the valve to the sealing position. Select the "Pressure Cook" or "Manual" setting and set the timer for 10 minutes on high pressure for chicken breasts or 15 minutes for chicken thighs.
Once the cooking time is complete, allow the pressure to release naturally for about 5-10 minutes. Then, carefully switch the valve to "Venting" to release any remaining pressure.
Open the Instant Pot lid and use two forks to shred the chicken directly in the pot. The chicken should be tender and easy to shred.
Thicken Sauce (Optional): If you prefer a thicker sauce, you can switch the Instant Pot back to "Sauté" mode and simmer the shredded chicken for a few minutes until the sauce thickens slightly.
Serve the BBQ shredded chicken on buns for sandwiches, over rice, or alongside your favorite sides. Enjoy!