No single feature defines California-style pizza aside from the willingness to break the rules and try something new. This is a gloss on the recipe that made California Pizza Kitchen famous.
1. Cut the chicken into pieces about ½-inch thick. (Too thin and it will dry out.) Mix the chicken with half of the barbecue sauce and chill.
2. Dissolve yeast and sugar in ¼ cup water. In a bowl, combine remaining ¾ cup water with 2 cups of flour and salt. When yeast bubbles, add to flour mixture. Stir and turn out onto a floured board. Let dough stand while you clean bowl. Coat inside of bowl with olive oil.
3. Knead dough 10 minutes, adding flour as necessary to make it silky. Return to bowl, cover with 2 tight layers of plastic wrap, and let rise in a warm place for 2 to 3 hours or until double in size.
4. Punch down dough and flatten on a well-floured board. Pound dough with heel of hand and lift to stretch it, methodically working dough into a circle about 14 inches in diameter. Sprinkle peel (a wooden pizza paddle) with cornmeal and place dough on it.
5. Sprinkle cornmeal on pizza stone; put in oven. Preheat to 500°F.
6. Spread the other half of the barbecue sauce across the dough, leaving a ½-inch un-sauced border. Sprinkle half the mozzarella over the sauce. Spread out the hoops of onion. Add the chicken, then the remaining mozzarella and the Gouda cheese.
7. Transfer pizza to baking stone in oven. Bake 10-12 minutes.