1. Remove dough from refrigerator. Let stand at room temperature, covered, for 30 minutes.
2. Place a pizza stone or heavy baking sheet in oven. Preheat oven to 500° (keep pizza stone or baking sheet in oven as it preheats).
3. Combine ketchup and next 8 ingredients (through onion powder) in a small saucepan; bring to a simmer. Reduce heat; cook 6 minutes. Combine 2 tablespoons ketchup mixture and chicken in a small bowl; toss to coat.
4. Roll dough into a 14-inch circle on a lightly floured surface; pierce liberally with a fork. Carefully remove pizza stone from oven. Sprinkle cornmeal over stone; place dough on stone. Spread remaining sauce over crust, leaving a 1/2-inch border. Arrange chicken mixture over dough. Sprinkle with cheese. Bake at 500° for 9 minutes or until crust and cheese are browned.
5. Combine vinegar, oil, and sugar in a medium bowl, stirring with a whisk. Stir in cabbage, onion, and carrot; toss to coat. Top pizza with cabbage mixture, parsley, and red pepper. Cut into 8 wedges.