Preheat oven to 475 degrees F. In a small bowl combine peanut butter, the warm water, sugar, vinegar, and 1/4 to 1/2 teaspoon crushed red pepper. Set aside.
In a medium skillet heat oil over medium heat. Add chicken; cook and stir for 3 to 4 minutes or until no longer pink. Add green onions and garlic; cook and stir for 1 minute more. Add 2 tablespoons of the peanut butter mixture. Cook and stir over low heat until chicken is coated. Remove from heat.
Coat a 12- to 14-inch pizza pan, large baking sheet, or pizza screen with cooking spray; set aside. On a lightly floured surface, roll bread dough into an 11- to 13-inch circle. Transfer to the prepared pizza pan. Spread dough with the remaining peanut butter mixture, adding water if necessary to reach spreading consistency. Top with chicken mixture, sweet pepper, and cheese.
Bake for 11 to 14 minutes or until cheese is melted and crust is lightly browned. Sprinkle with cilantro and, if desired, additional crushed red pepper.