Rub flank steak on both sides with 1/2 tsp salt and 1/4 tsp pepper. Place on a broiler rack 4 to 5-inches from heat for 3 to 4 minutes.
Turn and broil 3 to 5 minutes longer, to the desired degree of doneness. Transfer to a hot platter and dot with 3 Tbsp butter. Let stand in a warm place for about 5 minutes. Carve diagonally.
In a medium saucepan melt remaining butter and cook mushrooms, green onions, remaining salt and pepper about 10 minutes. Add white wine and cook briefly over high heat.
Add tomato, beef broth and tarragon. Cook, stirring occasionally, 5 minutes. Dissolve cornstarch in water and stir into sauce; cook and stir until thickened.
Serve over the sliced flank steak.
Servings: 6