Heat 1 tablespoon oil in each of 2 heavy large skillets over medium-high heat. Sprinkle steaks with salt and pepper. Add 3 steaks to each skillet; cook about 4 minutes per side for medium-rare. Transfer to platter; top each with 1 cheese wedge. Tent with foil to keep warm.
Pour off drippings from 1 skillet; add wine to skillet and boil over high heat until reduced to generous 1/2 cup, scraping up browned bits, about 5 minutes. Remove from heat; add butter and stir until melted. Mix in parsley and chopped chives. Season with salt and pepper. Pour over steaks. Garnish with whole chives.