Place a pizza stone in the oven and preheat to 500 degrees (or as high as your oven will go).
To make Peanut Sauce, combine all sauce ingredients in a small saucepan and bring to a boil. Boil gently for 1 minute. Remove from heat and set aside.
Heat olive oil in a nonstick pan and cook chicken until no longer pink, about 5 minutes. Place chicken in a bowl and toss with half of the peanut sauce.
Divide dough in half and shape each into a 9-inch round.
Coat a pizza peel lightly with cornmeal and place one pizza dough round on top. Spread 1/4 cup of sauce evenly on dough.
Cover sauce with 3/4 cup mozzarella cheese.
Place half the chicken on top of the cheese followed by half the green onions, carrots, and bean sprouts.
Top with 1/4 cup mozzarella and half of the peanuts.
Transfer pizza to pizza stone and bake 8 to 10 minutes, until crust is golden.
Sprinkle with cilantro and serve. Repeat for second pizza.