Heat oven to 350ºF.
Lay the flank steak on a piece of plastic wrap about twice its size and top with a second piece. Pound, using the flat side of a meat mallet, until the steak is about 1/4-inch thick.
Place the croutons, Parmesan, eggs, herbs, and garlic in the bowl of a food processor and pulse until it forms a paste.
Brush the pounded flank steak with 1 tablespoon of the vegetable oil and season with the salt and pepper. Spread the filling evenly over the meat. Roll tightly and tie with butcher's twine. Brush the outside of the roll with the remaining oil.
Place a 10-inch cast-iron skillet over medium-high heat for 3 to 4 minutes. Add the roll and sear on all sides until browned well, approximately 2 minutes per side. Carefully transfer to a 9-by-13-inch glass baking dish, add the tomato sauce, and roll the meat to cover. Tent the baking dish with aluminum foil so that the foil is not touching the meat. Cook for 45 minutes or the meat is done. Rest for 10 minutes in the dish before slicing and serving.