Prepare the udon noodles according to package instructions.
Heat sesame oil in a large skillet or wok over medium-high heat.
Add the sliced chicken (or tofu) to the pan and cook until golden brown.
Introduce the sliced vegetables, starting with the harder ones like carrots and broccoli.
Add the bell pepper and green onions, followed by the cooked udon noodles.
Pour in the soy sauce and oyster sauce (if using), stirring well to coat all ingredients.
Season with salt and pepper to taste, and stir-fry for an additional minute.
Serve hot, garnished with extra green onions if desired.