1. Cut the lemon in half again lengthwise, and then slice the wedges crosswise into paper-thin slices. Remove any seeds. Set aside.

2. Season the fillets lightly with salt and pepper, and dredge them thoroughly in flour. Shake off any excess flour.

3. Heat 2 tablespoons of the butter and the oil in a large skillet over medium-high heat. When the butter stops foaming, add the fillets. Cook, turning once, until golden and cooked through, 5 minutes. Transfer to dinner plates and keep warm.

4. Lower the heat under the skillet, and swirl in the remaining 1 tablespoon butter and the lemon slices. Sprinkle with the parsley, and season lightly with salt and pepper. Spoon the sauce over the fillets, and serve immediately.