4 servings
Source: Bon Appétit November 2005
Preheat oven to 350ºF. Melt 2 tbsp butter in heavy medium skillet over medium heat. Add shallots; sauté until soft, about 2 minutes. Add wine and cook until most of liquid evaporates, about 2 minutes. Add cream and simmer until sauce thickens slightly, whisking occasionally, about 4 minutes. Cut 4 tbsp butter into ½-inch cubes. Add cold butter to sauce, a few cubes at a time, whisking until incorporated before adding more. Whisk in lemon juice and season with salt and pepper. Remove from heat. Cover beurre blanc to keep warm while cooking fish.
Place mushrooms in blender; grind to fine powder. Transfer mushroom powder to plate. Sprinkle fillet with salt and pepper. Press fillet into mushroom powder to coat on all sides. Melt remaining 4 tbsp butter in large ovenproof skillet over medium-high heat. Add fillets to skillet; sauté until golden brown on bottom, about 3 minutes. Using large spatula, turn fillets over. Transfer to oven and cook until fillets are just opaque in the center, about 7 minutes longer.
Place 1 fillet on each of 4 plates, drizzle with beurre blanc sauce, and serve.