Season the flour generously with salt and pepper. Dust the sole fillets in the flour, shaking off any excess. Melt half of the butter in a large frying pan set over a medium heat and pan-fry the sole fillets for 2-3 minutes on each side until just cooked. Remove and arrange on a plate, covering it with aluminium foil to keep warm.
Make sure the pan is wiped clean, then add the remaining butter and melt until it starts to smell slightly nutty. Add the lemon juice and the spring onion.
Swirl to incorporate, then remove from the heat and season to taste. Arrange the sole fillets on serving plates and pour the sauce over. Garnish with a few sprigs of parsley leaves before serving.