Cut chicken to 1/2" pieces and marinate for 15 minutes with light soy sauce, sake, white pepper, salt and sesame oil.
Prepare the stir fry sauce by combining the light soy sauce, dark soy sauce, oyster sauce, mirin, white pepper, sugar, sesame oil and hot water in a bowl and mixing until combined.
Cut carrot, scallions, mushrooms, and cabbage to similar size pieces along with garlic and ginger and set aside.
In a pot of cold water, add the udon noodles until they become separated. Individually separate any strands of noodles that are still stuck together. Drain and set aside.
Over high heat, cook chicken in 1 tbsp oil until cooked through, about 3-4 minutes and set aside.
In the same pan, fry garlic and ginger for 15 seconds then add your vegetables and mix. Season with a teaspoon of kosher salt and continue cooking for another 2-3 minutes or until the vegetables are slightly wilted but still crisp.
Add back your chicken, udon noodles, and add your sauce and white pepper to taste. Continue cooking for 3-4 minutes over high heat until the sauce has thickened slightly. Stir in the scallion greens, top with sesame seeds and enjoy!
Notes
Preparing the Udon Noodles - If using frozen udon noodles, simply defrost them in cold water until pliable and separate them with your hands. If using fresh udon noodles, simply add them to the Yaki Udon (no need to boil). The heat will stir fry the noodles.After defrosting the udon noodles, drain them in a collander. I like to shake them dry and toss them in a tablespoon of neutral oil to prevent them from sticking while you prepare and cook the other ingredients.Sake - If you don't have sake or prefer to not use it, you can substitute with mirin or chicken stock/broth.Dark Soy Sauce - Dark soy sauce is thicker than "light" or "all-purpose" soy sauce; it adds color and a more intense flavor to the dish. Light (or all-purpose) soy sauce and dark soy sauce cannot be substituted with or for each other, as they're very different.Vegetables - In my Yaki Udon, I used sliced carrots, shiitake mushrooms, and cabbage. I like that each vegetable has it's own individual and unique flavor but work well together (none have too strong or overpowering flavor in relation to each other). They also cook and hold up well in high heat. You can also use baby bok choy, different kinds of mushrooms, zucchini, baby corn, broccoli, or bell peppers.Cut Ingredients into Similar Sizes for Even Cooking - I recommend cutting the chicken into 1/2" pieces - make sure each chicken piece is similar in size so they cook evenly. The same rule goes for the vegetables - cutting the vegetables into similar sizes will help them cook evenly in the hot wok or pan.Storage - You can store cooked Yaki Udon in an airtight container for up to 3-4 days in the refrigerator. When reheating, I like to reheat in the microwave with a wet paper towel on top to help loosen the noodles. Any leftover noodles will stick once stored in the refrigerator and lose some of its texture - but the delicious flavors of Yaki Udon will still be there!