Trim any excess fat off of the pork shoulder and cut into quarter pound chunks.
Combine the brown sugar, salt, black pepper, onion powder, garlic powder, and paprika in a bowl. Rub onto the meat covering on all sides.
Add the olive oil to the instant pot. Turn the instant pot onto saute mode for 15 minutes. Working in batches, sear the meat on all sides.
In a bowl combine the 1 cup of the beef broth, sriracha, Worcestershire sauce, and BBQ.
With all the meat removed from the instant pot, use 1/2 cup of beef broth to deglaze the instant pot.
Add the seared meat back to the instant pot and pour the wet ingredients over the meat. Cook on manual High pressure for 50 minutes and allow to naturally release for 20 minutes. Quick release the rest of the pressure. Shred with forks on a cutting board and return to sauce.
Notes
You can store your leftover pulled pork in an air tight container kept in the refrigerator for 3-4 days.