Heat 3 tablespoons of oil in a large skillet over high heat until it starts to shimmer. Add half the beef in an even layer. Let cook for a minute, undisturbed. Stir and cook for another 2 minutes or until the meat is browned. Remove to a plate and repeat with the rest of the steak. Remove that steak to the plate.
Add 2 tablespoons oil to the same pan and let heat. Add the peppers and cook, stirring occasionally until they start to blister, about 3 minutes. Add the garlic and ginger and cook, stirring, for 30 seconds. Add the sauce and deglaze the pan making sure to scrap up all the brown bits from the bottom of the skillet. Add the beef back into the skillet and cook stirring for another 1-2 minutes.