A classic French dish of sole.
Season fish with salt and dredge in flour, shaking off excess. Transfer to parchment lined baking sheet.
Work in batches if needed to prevent crowding. Heat 2 Tbsp. clarified butter in a large pan over medium-high heat until shimmering. Add fish and cook undisturbed until browned on the first side, 3-4 minutes. Carefully flip each filet and cook just until flesh is opaque, 30 seconds. Carefully transfer, browned side up, to plates and keep warm.
Wipe out skillet and add unsalted butter. Cook over high heat, swirling occasionally, until butter browns, 1-2 minutes.
Squeeze lemon juice over fish and sprinkle with parsley. Spoon browned butter over top and serve immediately with additional lemon if desired.