Heat the oil in a large saucepan over medium-high heat. Cook and stir the chicken, about 3 to 4 minutes, until no longer pink.
Add the cabbage, pepper, carrots, and peas and cook, stirring occasionally, for 2 to 3 minutes, or until the veggies are slightly softened.
Add the garlic, ginger, salt, and chili flakes (more or less according to your tastes) and cook for 1 minute.
Stir in the broth, soy sauce, and hoisin sauce and bring to a simmer. Add the noodles and reduce the heat to medium-low.
Cover and cook, stirring every couple of minutes so the pasta doesn’t stick together, until al dente, about 4-6 minutes.
If desired, combine the cornstarch and water in a small bowl and stir into the sauce to thicken.
Taste, adjust seasonings according to your preferences (add 1 tablespoon honey to sweeten if desired), and serve.
