Trim leeks and cut into thick rings, 1 1/2 to 2 inches. Wash in sink of cold water to free grit and dry in batches on kitchen towels.
Heat a large, deep skillet over medium heat. Melt butter and add leeks, season with salt and sauté to wilt a few minutes. Douse leeks with wine and reduce a minute then place lid on pan and cook 5 minutes more.