Rub the fillets with the chopped tarragon and pepper. Melt 2 TBS of the butter in a large skillet over medium high heat. Add the fillets and cook for 4 to 5 minutes on each side or to the desired degree of doneness. Remove from the skillet and keep warm.
Melt the remaining 3 TBS butter in the skillet. Add the mushrooms. Saute for 3 to 4 minutes or until tender. Add the wine. Cook for 1 to 2 minutes, stirring to deglaze the skillet. Stir in the sour cream. Add 1/4 cup of the cheese. Cook until melted, stirring constantly.
To serve, drizzle the sauce over the fillets. Sprinkle with the remaining cheese. Garnish with sprigs of tarragon.