Cut the chicken into bite-sized pieces and mix with salt, soy sauce, mirin, and cornstarch. Massage to help the flavors absorb, then let it rest for 10 minutes.
Bring a pot of water to a boil. Add the udon and stir gently until the noodles loosen up. Drain and set aside.
Heat a pan over medium heat with oil. Add the chicken, spread it out in a single layer, and let it brown. Stir-fry until fully cooked.
Toss in the onion and bell peppers. Stir-fry for about a minute, keeping the veggies crisp and colorful.
Add the loosened udon noodles, then season with soy sauce, dark soy sauce, and plenty of freshly ground black pepper. Toss until everything is evenly coated and glossy. Garnish with chopped green onions and enjoy hot.