Marinate the chicken: In a bowl, combine soy sauce, sesame oil, mirin, garlic, ginger, and rice vinegar. Add the chicken and marinate for at least 2 hours (or overnight for deeper flavor).
Prepare the vegetables: Slice zucchini, onions, and mushrooms into uniform pieces. Toss with a little oil, salt, and pepper.
Preheat the Blackstone griddle to medium-high heat (around 400°F). Lightly oil the surface.
Cook the chicken: Place the marinated chicken on the hot griddle. Cook for 3-4 minutes per side, or until golden brown and the internal temperature reaches 165°F.
Cook the vegetables: Move the chicken to a cooler zone of the griddle. Add the prepared vegetables to the hot zone. Stir-fry for 3-5 minutes until tender-crisp.
Heat the rice: Place the cooked rice on a cooler zone of the griddle to warm it up while finishing the chicken and vegetables.
Combine and serve: Return the chicken to the hot zone to reheat briefly. Serve the chicken and vegetables over warm rice, optionally drizzled with Yum Yum Sauce or Ginger Garlic Sauce.