In a large skillet, saute mushrooms in 1 tablespoon butter until tender; set aside., In a small bowl, beat the cream cheese, 1 cup Gruyere cheese, 2 tablespoons chives, tarragon, garlic, salt and pepper until blended. Spread over bread slices. Spoon mushrooms over half of the slices; place remaining bread slices over the top, spread side down., In a shallow bowl, whisk the eggs, milk and melted butter. Dip both sides of sandwiches into egg mixture., In a large skillet, toast sandwiches in remaining butter in batches until golden brown, 2-3 minutes on each side. Sprinkle with remaining cheese and chives.