Slice steak into ½-inch thick slices across the grain.
Whisk together soy sauce, sugar, cornstarch, and ginger in a bowl until smooth. Add beef and coat well.
Heat 1 tablespoon oil in a wok or skillet over medium-high heat. Stir-fry beef in batches until browned, about 3 minutes. Set aside.
Return all beef to wok. Add onion and stir-fry for 2 minutes until it begins to soften.
Add green pepper, cook 2 minutes until tender-crisp.
Add tomatoes, stir to combine and heat through. Serve.
