Whisk together all yum yum sauce ingredients in a small bowl. Thin with water to desired consistency. Refrigerate until serving.
Heat griddle over medium-high heat until very hot. Add 1/2 tablespoon sesame oil and 1/2 tablespoon butter.
Scramble the egg directly on the griddle. Add cooked rice and peas and carrots. Season with soy sauce, garlic powder, onion powder, and sesame oil. Stir-fry 3 to 4 minutes until rice is lightly toasted. Push to one side.
Add butter and sesame oil to the cleared section of the griddle. Add zucchini, onion, mushrooms, and broccoli. Season with soy sauce, garlic powder, salt, and pepper. Stir-fry 4 to 5 minutes until tender but slightly crisp. Sprinkle with sesame seeds if using. Push to the side.
Add remaining butter and sesame oil. Add chicken pieces and season with salt, pepper, onion powder, and garlic powder. Stir-fry 5 to 6 minutes until golden brown and cooked through. Add soy sauce and teriyaki sauce if using in the last minute. Toss to coat.
Plate chicken, fried rice, and vegetables together. Serve yum yum sauce on the side.