Combine flour, 1 tablespoon fines herbes, and 1/4 teaspoon salt. Season fish with salt and pepper and dredge in flour to coat, shaking off excess. In a large non-stick skillet heat 1 tablespoon butter over moderately high heat until foam subsides and cook fish 3 minutes each side, or until just cooked through.
Reduce heat to moderately low. Cut remaining butter into pieces and add to skillet. Simmer butter until golden brown with a nutty aroma, about 5 minutes. Remove skillet from heat and immediately add lemon juice, salt, remaining herbs and pepper to taste, swirling skillet to incorporate (butter will foam.) Serve sole filets with butter.
Recipe courtesy Sara Moulton