For the marinated steak: Combine the fish sauce, ginger, garlic, honey, lime juice and 1 tablespoon of the sliced scallions in a bowl and whisk to combine. Add the steak and toss well to coat.
For the stir-fry: Mix the remaining sliced scallions with the garlic and ginger in a small bowl and set aside.
Heat a large nonstick saute pan or wok over high heat. Add 1 tablespoon of the vegetable oil and half of the steak. Spread into a single layer and let sear 30 seconds. Toss the meat, spread back out and sear again, another 1 1/2 to 2 minutes. Toss once more and remove to a serving dish. Return the pan to the heat until hot. Add another tablespoon vegetable oil and the remaining meat and repeat.
Return the pan to the heat until hot. Add another tablespoon of oil and half of the reserved garlic, ginger and scallion mixture. Cook the aromatics for about 30 seconds, then add half of the vegetables and cook, adding 1 to 1 1/2 tablespoons soy sauce and about 2 ounces of water to the pan as the vegetables cook, about 4 minutes. Transfer to the serving dish. Wipe out the pan, return to the heat, add the remaining tablespoon oil and repeat with the remaining aromatics, vegetables and soy sauce. (Make sure to reheat the pan completely between batches.)
Toss the meat and vegetables together in the serving dish and serve with steamed white rice.
Slice the steak thinly and evenly for a quick cooking time. Leftovers make great lettuce wraps!