Heat 1 tablespoon of oil in a large skillet.When the pan is nice and hot (almost smoking) add in half of the steak. Cook for 1-2 minutes on each side. Keep an eye on it to make sure it doesn't get too brown.Remove the steak from the pan. Repeat with the remaining steak and set aside.
If there isn't enough oil left in the pan add a bit more and saute the peppers until tender, 3-4 minutes.Add in the garlic and ginger and cook for an additional minute.
Stir in the soy sauce, water, rice vinegar and pepper. Bring to a simmer.
Remove 1 tablespoon of the cooking liquid and mix with the cornstarch. Slowly add the cornstarch mixture back to the pan and simmer until thickened.
Add the steak back to the pan and toss to coat in the sauce.
Serve immediately with sesame seeds and green onions, if desired.