Whisk together soy sauce, sugar, cornstarch, and ginger in a large bowl until the sugar is dissolved and the mixture is smooth. Place the steak slices in the marinade and stir until well coated.
Heat 1 tbsp of the vegetable oil in a wok or large skillet over medium high heat and place 1/3 of the strips into the hot oil; cook and stir until the beef is well browned. Remove beef and place in a large bowl. Repeat this step 2 times more setting cooked beef aside.
Return all the cooked beef to the hot skillet and stir in the onions. Toss the beef and the onions ;until the onions soften; then stir in the green peppers. Cook and stir the mixture until the pepper has turned bright green and starts to become tender then add the tomatoes. Stir everything together and serve.