Prepare the Sole: Season the sole fillets with salt and pepper. Dredge the fillets lightly in flour, shaking off any excess.

Cook the Sole: In a large skillet, melt 2 tablespoons of butter over medium-high heat. Once the butter is foaming, add the sole fillets. Cook for 2-3 minutes per side or until golden brown and the fish flakes easily with a fork. Be gentle when flipping the fillets to prevent them from breaking. Transfer the cooked fillets to a warm plate.

Make the Sauce: In the same skillet, add the remaining 2 tablespoons of butter. Cook until the butter turns a light brown color and has a nutty aroma. Remove the skillet from the heat and stir in the lemon juice and parsley. Season with salt and pepper to taste.

Serve: Pour the sauce over the sole fillets. Garnish with lemon slices and additional parsley if desired. Serve immediately, traditionally with steamed potatoes or green vegetables.