Scale the skin and rub the fish clean with a moist towel. Fillet out both sides of the centercut, leaving the bones behind, and run your finger along the meat side of each fillet to identify and complete the small bone removal with kitchen pliers.
Combine the salt, sugar, and pepper in a bowl and mix thoroughly. In a large glass roasting dish or earthenware platter, place the fillets skin side down and side by side. Rub the surfaces with half of the salt mixture. Spread the fresh dill thickly over the exposed surface of one fillet, and then cover, meat side down, with the other fillet. Rub the remaining salt mixture over the skin sides of the fillets.
Tightly cover the fillets and the glass dish with aluminum foil so there are no air holes. Place a light weight on top of the fillets, and refrigerate for 48 hours. After the first 4 hours the fluid should be poured off the gravlax, and then resealed and refrigerated.
To serve, position the fillet skin side down, and cut paper thin slices on a bias, leaving the skin behind. Serve each morsel on thin slices of rye bread, as with smoked salmon, and accompany with horseradish mustard sauce.