Use your fingers to press the pepper onto both sides of the steaks. In a very large skillet cook steaks in hot oil over medium heat 10 to 12 minutes or to desired doneness, turning once halfway through cooking time. Transfer steaks to a serving platter, reserving the drippings in the skillet. Keep warm. Remove skillet from burner.
Carefully stir wine and broth into drippings in the skillet, scraping up crusty browned bits. Return to burner. Bring to boiling; add chard. Cover and cook until wilted and tender or about 5 minutes for chard or 2 to 3 minutes for spinach, stirring occasionally.
To serve cut steak into serving-size pieces. Serve chard or spinach with steaks.