Step 1

Slice the steak into 1/2-inch thick slices across the grain.

Step 2

Whisk together soy sauce, sugar, cornstarch, and ginger in a bowl until the sugar has dissolved and the mixture is smooth. Place the steak slices into the marinade, and stir until well-coated.

Step 3

Heat 1 tablespoon of vegetable oil in a wok or large skillet over medium-high heat, and place 1/3 of the steak strips into the hot oil. Cook and stir until the beef is well-browned, about 3 minutes, and remove the beef from the wok to a bowl. Repeat twice more, with the remaining beef, and set the cooked beef aside.

Step 4

Return all the cooked beef to the hot wok, and stir in the onion. Toss the beef and onion together until the onion begins to soften, about 2 minutes, then stir in the green pepper. Cook and stir the mixture until the pepper has turned bright green and started to become tender, about 2 minutes, then add the tomatoes, stir everything together, and serve.