Sauteed Skirt Steak with Braised Scallions

Put oven rack in middle position and preheat oven to 200 °F. Pat steaks dry and sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat oil and 1 tablespoon butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then cook steaks, turning over once, 5 to 7 minutes total for medium-rare. Transfer steaks to a plate and keep warm in oven. Discard fat from skillet, then add water and bring to a boil, scraping up brown bits from bottom of skillet. Add scallions and remaining tablespoon butter, 1/2 teaspoon salt, and 1/4 teaspoon pepper and cook, tightly covered, over moderate heat until scallions are tender, 5 to 7 minutes. Transfer scallions with tongs to a platter and put steaks on top. Pour any steak juices accumulated on plate into juices in skillet and boil until slightly thickened. Add lime juice and pour sauce over steaks and scallions.