Cut pita in half to form 2 pockets. Mix together mayonnaise, barbeque sauce, and prepared horseradish (if using). Spread some of the sauce mixture in each of the pockets and top with half of the remaining ingredients.
I prefer to grate my own cheese when preparing dishes that call for it. The fresh grated cheese is not coated with the “anti caking agents” that they apply in the factory to keep it from sticking together. I think this helps you to taste more of the cheese flavor, and you can use less of the other condiments that you normally apply to glue everything together.