Rub fillets evenly with chopped thyme and pepper.
Melt 1/4 cup butter in a large skillet over medium-high heat. Add fillets, and cook 5 to 6 minutes on each side or to desired degree of doneness. Remove from skillet, and keep warm.
Melt remaining 1/4 cup butter in skillet. Add sliced mushrooms, and sauté 3 to 4 minutes or until tender. Add wine, and cook 1 to 2 minutes, stirring to loosen particles from bottom of skillet. Stir in sour cream and 1/4 cup cheese until melted. Drizzle sauce over fillets; sprinkle with remaining cheese. Garnish, if desired.