Preheat oven to 400ºF.
Place pitas on two baking sheets. Spread about 2 tablespoons of barbecue sauce evenly on each pita, and sprinkle with cumin. Then add the toppings - feta cheese, shallot, black beans, and pineapple - and crush dried rosemary over the top.
Bake for 10 minutes, or until desired doneness is reached.