Filling: Trim the both ends of the leeks, removing the tough, green end. Slice the leeks in half lengthwise and rinse thoroughly (leeks can be very dirty). Slice the leeks widthwise into 1/4 inch (approx) half moons. In a large frying pan over medium heat melt the butter. When melted, add the leeks, season with salt and pepper, add the thyme, and cook (stirring frequently) until softened (approx 10 minutes).