Cook the noodles according to the directions on the package. Set aside.
Season the chicken with salt and pepper.
Heat a nonstick pan over medium high heat. Once hot, add the oil and brown the chicken well. Then remove from the pan and set aside.
Turn down the heat to medium and add the onions and peppers to the pan. Saute until soft. Then add the garlic and ginger. Saute until golden brown. Stir in the vinegar, soy sauce, oyster sauce, broth, and broccoli. Cover with a lid and bring to a simmer until the broccoli is tender and the flavor concentrates. (Add brown sugar as needed to sweeten if desired)
Remove the lid and toss in the chicken and scallions. Taste and adjust any of the seasonings. Simmer until the sauce has a thick consistency (if needed to thicken the sauce more stir in the cornstarch/water slurry a little at a time until it reaches the desired consistency.
Toss with the noodles right before serving. Garnish with scallions and red pepper flakes if desired.