Prepare a hot grill outside or preheat a grill pan to high heat and preheat oven to 375 degrees F.
Toss raw chicken in a bowl with rub, a few pieces at a time until all chicken is well coated. Grill chicken on well oiled grill or grill pan for about 2 minutes on each side, until nice grill marks are formed. If chicken pieces are very thick, finish cooking for 5 to 10 minutes more in the preheated oven. Allow chicken to cool a few minutes and then pull apart into nice shreds. Toss chicken with BBQ sauce so that it is well coated but not overly wet. Keep warm in a warm saute pan until ready to use.
Heat olive oil in large saute pan over medium-high heat. Stir in garlic with wooden spoon. After 30 seconds add spinach and turn off heat. Toss spinach in hot oil, when wilted completely season with salt. Set aside.
Spread butter evenly over 1 side of each pita. In a large saute pan, grill each flatbread over medium-high heat, buttered side down (work in batches if necessary) top each flatbread with 1 1/2 ounces of cheese, 1/4 of the spinach, and 1/4 of the chicken. Fold each flatbread over and continue grilling until golden brown on each side. Cut in half crosswise, transfer to platter and serve.
Combine all ingredients, using a whisk, wooden spoon or hands. Use hands to break up lumps of brown sugar.
Heat oil n a 1-gallon saucepan over medium heat, sweat onions until translucent, about 5 to 10 minutes. Add garlic and sweat 1 more minute. Add dry spices and BBQ rub; stir. Cook until spices become fragrant, about 1 minute more. Add remaining ingredients and simmer slowly for 20 minutes. Using an immersion blender, puree sauce until smooth.
Recipe courtesy of Adam Gertler