Season flour with salt and pepper to your preference, then dredge fillets in the mixture, shaking off any excess.
Heat 2 tablespoons clarified butter in a large saute pan. When heated, place fillets in pan and cook over medium heat for 2 to 3 minutes per side, until golden brown and crispy. Remove fillets from pan and transfer to a platter; sprinkle with parsley, then cover with foil.
Remove remaining butter from the skillet and add the fresh butter. Heat until the butter begins to brown. Remove from heat and stir in lemon juice and capers. Pour sauce over fish and serve. Garnish with lemon slices.