These BBQ chains serve pulled pork and cornbread that diners say belong together. I prefer a pulled pork plate, so I can eat my carbs in the form of cornbread instead of a roll. Here are 5 BBQ chains with the best pulled pork and cornbread, according to diners. Mission BBQMission BBQ, one of my favorite chains for delicious BBQ pulled pork. Dickey’s Barbecue PitDickey’s Southern Pulled Pork is slow-cooked pork shoulder, smothered in the chain’s trademark BBQ sauce, that diners order on repeat.