Season the sole fillets with salt and pepper, then dust with flour on both sides, shaking the excess off.
In two large nonstick skillets, or in a double-burner nonstick griddle, 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. You might need to lower the heat to medium after turning, depending on how hot your pan gets.
Transfer the fish to plates. Garnish with parsley and lemon wedges. Serve immediately.
Notes
Nutrition info if using almond flour: calories 284, fat 15g, saturated fat 4g, sodium 432mg, carbs 3g, fiber 1g, sugars 0g, protein 34g.