Combine all ingredients in a medium saucepan and bring to a boil over medium heat. When the mixture is boiling, simmer it for about 5 minutes, whisking frequently, until the sauce is thickened and smooth. Remove from heat and cool completely.
Make the pizza:
Preheat the oven to 450° F and sprinkle a thin layer of semolina flour on a pizza pan.
Gently stretch the dough into a circle about 12-14” in diameter and place the dough on the prepared pizza pan. Bake for 8 minutes, until lightly golden.
Spread hoisin sauce in an even layer over the surface of the par-baked pizza dough.
In a medium bowl, toss together chicken and peanut sauce until chicken is coated. Spoon chicken in an even layer over the pizza. Sprinkle the grated carrot over the pizza followed by the cheese. Bake for about 15 minutes, until the cheese is melted and the crust is deeply browned.
Remove from the oven and top with sliced red onion, chopped green onions, fresh cilantro, and peanuts. Drizzle withTy Ling Hot Mustard and serve.