Place pork shoulder roast in the bottom of the Instant Pot. Pour 1/2 cup chicken broth (or water) in with the roast.
In a mixing bowl, combine bbq sauce, apricot preserves, dry onion soup mix, Dijon mustard, and soy sauce.
Pour sauce on top of roast.
Place the lid on top of the Instant Pot and move the valve to SEALING. Press the MANUAL (PRESSURE COOK) button and set timer for 60 minutes (or 20 minutes per pound, depending on the size of your roast).
When the timer is done, let the pressure do a NATURAL RELEASE (it will take at least 20 minutes, but I even prefer to let the roast sit in there for a couple hours to make sure it is super tender).
Remove the lid and shred the roast with 2 forks.
Place the shredded meat back into the sauce and mix together so that all of the meat is covered.
Place meat on hamburger buns or rolls and serve.