Make the marinade: Whisk together the soy sauce, pineapple juice, brown sugar, vinegar, garlic, and ginger in a medium bowl. Set aside ½ cup of the marinade for the serving sauce.
Place the steaks in a large zip-top plastic bag. Pour the large amount of the marinade over the steaks in the bag. Press out any excess air and seal the bag. Place in a baking dish and refrigerate for 8 hours or overnight.
Whisk together the reserved ½ cup marinade and the cornstarch in a small saucepan. Place over medium heat and bring to a boil, whisking frequently. Cook 2 minutes or until the sauce is thickened. Set aside.
Preheat the a charcoal or gas grill to medium-high heat. Remove the steaks from the marinade, and discard the marinade. Grill the steaks 3 to 4 minutes on each side or desired degree of doneness. (Use a meat thermometer to check internal temperature. Medium-rare steak will be 130°F to 135°F)
Grill the pineapple wedges and green onions while the steak cooks until charred and tender.
Remove the steaks, pineapple, and green onions from the grill. Let the steaks rest for about 15 minutes before slicing thinly against the grain. Transfer steaks to a serving platter with the pineapple wedges. Slice the green onions and sprinkle on top. Serve with the reserved thickened sauce on the side.