Heat 2 tablespoons clarified butter in each of 2 large saute pans.
Dredge fillets in flour, shaking off any excess flour. Place fillets in saute pans and cook over medium heat for 2 to 3 minutes per side, until golden brown and crispy. Remove fillets from pans and transfer on to a platter, sprinkle with parsley. Cover with foil.
Remove remaining butter from one of the skillets 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.