In a large skillet cook the leek in 2 tablespoons of the butter over medium heat for 2 minutes. Add the potatoes. Reduce heat to medium-low. Cook and stir for 8 to 10 minutes or until potatoes are tender, crisp, and golden. Remove potato mixture from skillet to a medium bowl; set aside.
In the same skillet heat the remaining butter over medium heat. Add the mushrooms. Cook and stir for 5 to 6 minutes or until tender and liquid evaporates. Stir in the 2 tablespoons parsley, tarragon, salt, and pepper until combined. Stir in potato mixture and heat through. Transfer to a serving dish. Sprinkle with additional parsley. Makes 4 servings.