1. Place the salmon skin side down on a large tray. Using tweezers, remove any small bones. Using a large cooking fork, pierce the salmon all over every few inches. Sprinkle the salmon with the sugar, salt, and pepper.
2. In a small bowl, combine the dried and fresh dill with the oil. Spread evenly over the salmon. Cover the salmon with plastic wrap and refrigerate for 3 days.
3. Remove the gravlax from the refrigerator and scrape away the dill. Slide it onto a large serving tray or board. Slice the gravlax very thin on a diagonal.
4. To serve, garnish the gravlax with fresh dill sprigs or lemon leaves. Serve it with the Dill Mustard Sauce, rye bread, and butter on the side.
Note: To prevent damaging the salmon, ask the fishmonger to place it flat, without folding, on a piece of cardboard for support.