In a plastic re-sealable bag, combine black pepper, salt, paprika, cumin, brown sugar, cayenne pepper, allspice, 2 teaspoons of ginger, and the chopped parsley. Add flank steak and coat evenly. Seal bag and refrigerate for 1 to 12 hours.
Grill for 8 to 10 minutes. Allow meat to rest 10 minutes before slicing.
In a small non-reactive bowl, combine sesame oil, rice wine vinegar, soy sauce, and sugar. Stir until sugar dissolves. Add remaining ginger and jalapeno. In a wok pan, combine dressing and scallions.
Cook 1 to 2 minutes. Add cabbage and carrot and toss until heated through, about 3 to 4 minutes.
Remove from heat and add cilantro.
Combine sliced flank steak and cabbage slaw and serve on warm pita wraps.