Preheat a large griddle or large skillet over high heat. Brush the meat with extra-virgin olive oil, you'll need about 1/4 cup. Sear the steaks 2 minutes on each side, 3 at a time. Arrange steaks on baking sheet. When steaks are all seared off, transfer to oven and roast 5 to 6 minutes for medium doneness, subtract or add 2 minutes to that time for medium- rare to medium-well.
Place tomatoes on a broiler pan and season with salt and pepper. Combine the bread, olives, parsley, sage and Romano in the food processor and pulse grind the mixture. Dress the mixture with some extra-virgin olive oil salt and pepper and fill the tomatoes.
Dress chopped arugula and basil with a little lemon juice, extra-virgin olive oil, and salt and pepper.
Remove steaks and let rest. Switch broiler on and broil tomatoes a couple of minutes to brown the cheese and bread crumbs on top.
Serve steaks with greens on top and broiled tomatoes alongside.