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.