For the dry rub: Mix together the paprika, black pepper, salt, brown sugar and cayenne pepper.
For the pork: Sprinkle the dry rub all over the pork tenderloins and place in a resealable plastic bag. Refrigerate for at least 2 hours, and then bring to room temperature before cooking.
Cut each tenderloin into 2 or 3 large pieces. Heat the oil in a large soup pot or Dutch oven. Sear the pork on all sides in batches (you don't want to overcrowd the pan), 4 to 5 minutes. Cover with the apple juice, vinegar, BBQ sauce, garlic and ginger. Bring to a simmer over medium-high heat, and then cover and simmer for 30 minutes, turning occasionally.
Transfer the pork to a clean cutting board and shred using 2 forks. Place the shredded pork back into the pot and continue to cook over medium-low heat, uncovered, just to heat through, 10 minutes longer.
Serve on hamburger buns topped with BBQ sauce and coleslaw with mustard and pickles, if desired.
Recipe courtesy of Bobby Deen