Special equipment: an Instant Pot® multi-cooker
Combine paprika, mustard powder, cumin, 1 tablespoon brown sugar, 2 teaspoons salt and 1/2 teaspoon pepper in a small bowl. Rub the spice mixture all over the pork.
Turn the Instant Pot® (see Cook's Note) to the high saute setting. Add the oil and once hot, add the pork and cook in two batches, turning, until browned on all sides, about 5 minutes. Switch the Instant Pot® to the warm setting, remove the pork and transfer to a plate.
Whisk 3/4 cup water into the drippings in the Instant Pot®. Add the vinegar, tomato paste, the remaining 2 tablespoons brown sugar and 2 cups water and whisk to combine. Add the pork back. Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on high for 1 hour.
After the pressure cook cycle is complete, follow the manufacturer's guide for quick release and wait until the quick release cycle is complete. Careful of any remaining steam, unlock and remove the lid and transfer the pork to a large bowl.
Switch the Instant Pot® to the normal saute setting and simmer the juices until reduced by half, about 15 minutes. While the juices are reducing use a ladle to remove any fat that rises to the top. Season to taste with salt.
Meanwhile, use 2 forks to shred the pork in to small chunks.
Add 3 cups of the reduced cooking liquid to the chunked pork and season with salt and vinegar to taste. Serve in hamburger buns with barbecue sauce and coleslaw.
Settings may vary on your Instant Pot® depending on the model. Please refer to the manufacturer's guide.
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