Stir together brown sugar, salt, chili powder, paprika, garlic powder and pepper in small bowl. Season pork shoulder all over with dry rub, reserve any leftover rub.
Spray 6-quart electric multicooker pot with cooking spray. Select sauté function and place pork in pot in single layer. Cook 10 minutes, undisturbed until browned on one side. Whisk together tomato paste, broth, vinegar, mustard and any remaining spice rub in small bowl. Turn pork and pour broth mixture over.
Turn off multicooker. Lock lid in place and close pressure release valve. Select high pressure cook function and set timer for 1 hour. When time is up, carefully open valve to quick release steam. Carefully remove lid. Shred pork with 2 forks. Remove pork with a slotted spoon and serve pulled pork on buns with BBQ sauce and pickles.
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