Heat the oil in a saucepan over medium heat.
Add the jackfruit and chiles and cook, stirring, for 3 minutes.
Stir in the barbecue sauce, tamari, mustard, paprika, liquid smoke, onion powder, and salt and pepper to taste.
Cook, stirring occasionally, to heat through and blend the flavors, about 8 minutes.
Mix well, adding a little water if the mixture is too dry.
Taste and adjust seasonings, if needed.
When ready to serve, spoon the mixture onto the rolls and serve hot.