Sprinkle fillets with salt and pepper. Melt 1 T. butter in a 10-inch skillet over medium-high heat. Add fillets and cook 4 minutes on each side; remove from skillet, reserving drippings in skillet, and keep fillets warm. Reduce heat to low.
Melt 1 T. butter with hot drippings in skillet; add mushrooms and shallots, and saute 4 minutes. Sir in 1/2 c. wine; cook over high heat 5 minutes.
Combine flour and 1 t. softened butter; stir to form a smooth paste. Add to mushroom mixture; cook, stirring constatnly, 30 seconds. Add remaining 1 T. butter and 2 T. wine; stir until butter melts. Spoon sauce over fillets. Serve immediately.