Add all ingredients for the bbq sauce to a large saucepan. Whisk to combine and heat over medium. Bring to a full (but controlled) boil. Reduce the heat and allow sauce to simmer, stirring occasionally, for 20 to 30 minutes, until thick.
Remove saucepan from heat and allow it to cool. The sauce will continue to thicken as it cools. Transfer sauce to a sealable container and refrigerate until ready to use. Sauce will keep for up to 3 weeks.
Prepare the Pulled Pork:
Remove the webbing from the pork shoulder roast and place on a cutting board. Chop the roast into 2-inch cubes and trim off any excess fat.
Add 1 cup of the BBQ sauce and the broth to the Instant Pot and stir well. Add the cubed pork and stir until pork is well-coated. Sprinkle with sea salt.
Secure the lid of the Instant Pot and turn the vent lid to "sealing" Turn the Instant Pot on the High Pressure Cook setting for 60 minutes. Once the time is up, allow the vent to naturally release.
Open the lid and using a slotted spoon, transfer the pork meat to a cutting board. Use two forks to shred the meat, then transfer it back to the Instant Pot. Secure the lid (turn the Instant Pot off or put it on Keep Warm) and stir well. Let meat sit for at least 10 minutes (up to 2 hours) to allow the meat to absorb the juices.
Serve pulled pork as a sandwich, bowl-style with your favorite ingredients, or on top of a green salad.