In a small bowl, combine mayonnaise, 2 chilies seeded and finely chopped, 1 teaspoon adobo sauce and lime juice. Season with black pepper. Keep chilled until ready to serve. Makes about 1/2 cup. (The mixture may be made up to three days in advance.)
Form pockets in halved pitas. Pit and slice avocado. Divide mayonnaise mixture and spread a spoonful deep inside each pocket. Divide turkey, cheese and avocado slices among pockets, tucking them inside. Divide sprouts among the pockets. Spread remaining mayonnaise on top. Wrap in foil and refrigerate.