In a small mixing bowl, combine 1 cup water, 3 tablespoons soy sauce, 3 tablespoons oyster sauce, 1 tablespoon lime juice or rice vinegar, and 1 tablespoon brown sugar. Whisk until well combined and set aside.
In a large skillet or wok, heat 1 tablespoon sesame oil over medium-high heat. Add 1 pound ground chicken and cook until browned, about 5-7 minutes, breaking it apart with a spatula.
Once the chicken is cooked, add 8 ounces sliced mushrooms, 1 bell pepper sliced thin, and the white parts of 1 bunch scallions to the skillet. Stir-fry for another 3-4 minutes, until the vegetables start to soften.
Next, add the 18-20 ounces vacuum-packed udon noodles to the skillet. If necessary, rinse the noodles under warm water to separate them. Toss everything together to combine.
Pour the prepared sauce over the chicken and noodle mixture, then add 1 cup mung bean sprouts. Stir well to ensure everything is evenly coated in the sauce. Allow it to cook for an additional 2-3 minutes, stirring occasionally.
Remove the skillet from heat. Serve your Chicken Yaki Udon hot, garnished with the green parts of the scallions. Enjoy this delightful dish with your favorite beverage!