In a large mixing bowl, combine the ground beef, breadcrumbs, milk, chopped onion, minced garlic, soy sauce, Worcestershire sauce, brown sugar, ground ginger, salt, and pepper. Mix until well combined.
Divide the mixture into equal portions and shape them into oval-shaped patties.
Heat the vegetable oil in a skillet over medium heat. Once hot, add the patties to the skillet and cook for about 5-6 minutes on each side, or until they are browned and cooked through.
While the patties are cooking, prepare the sauce. In a small saucepan, combine the remaining soy sauce, Worcestershire sauce, brown sugar, and ground ginger. Bring to a simmer over medium heat, stirring occasionally, until the sauce thickens slightly.
Once the patties are cooked through, pour the sauce over them in the skillet, coating them evenly.
Allow the patties to simmer in the sauce for an additional 2-3 minutes, until heated through and the sauce has thickened.
Remove the patties from the skillet and transfer them to a serving platter.
Garnish with thinly sliced green onions before serving.
Serve the Hawaiian Chopped Steak hot, accompanied by steamed rice and your favorite side dishes.