Season the sole filets with salt and pepper, then dust with flour on both sides, shaking off any excess flour.
In a large nonstick skillet, melt the butter over medium-high heat. When foaming subsides, add the fish.
Cook the fish, turning once with two wide spatulas, until golden-brown, about 3 minutes on each side. If one side gets too dark, reduce the heat to medium.
Transfer the fish to a plate, garnish with parsley and lemon wedges. Serve immediately.
