In a heavy medium skillet melt the butter over high heat When the butter begins to brown add the mushrooms and toss to coat
Saute stirring occasionally until the mushrooms have browned around the edges 2 to 3 minutes
Add the green onions and cook for 1 minute longer Transfer the mushrooms to a plate and season with salt and pepper
Divide the cheese among 4 slices of bread
Top each with the mushrooms leaving about 14-inch from the edge of the bread Add a tarragon sprig and cover with the remaining 4 slices of bread
Preheat a cast-iron ridged griddle or skillet for 10 minutes over moderate heat Grill the sandwiches for 4 minutes per side or until the bread is lightly browned and the cheese has melted
Serve halved as a first course or quartered as an hors doeuvre