Combine the salt and sugar, and rub the flesh side of the fish with the mixture. Place one fillet skin side down in a deep dish. Add pepper, fresh dill, and caraway seeds. Place the other fillet skin side up on top. Cover the dish with plastic wrap and place a weight on top of the fish. Refrigerate for 3 to 4 days, turning the fish every 12 hours and basting it with the brine that accumulates in the dish.
To serve, discard the brining liquid and brush off the dill. Slice the fish into thin slices. Serve with mustard sauce.