Separately, melt the butter in a large non-stick skillet over medium heat. Add-in the leeks, thyme and sprinkle a bit of salt and pepper on top. Cook until the leeks are ten-der, but not browned. Make sure to stir frequently for about 10 minutes. Last, combine with the diced mushrooms and continue to sauté for about 3 more minutes. When ready, remove from heat and set aside.