Combine the salt, sugar, and cracked black pepper in a mixing bowl. Transfer half the mixture to a nonreactive pan or baking dish that is large enough to hold the salmon. (If you don’t have a large enough baking dish, line a rimmed baking sheet with enough plastic wrap to wrap around the salmon twice, and place half the mixture on the plastic wrap.)
Place the salmon, skin side down, on the salt mixture. Cover the flesh side of the salmon with the remaining salt mixture, rubbing it onto the salmon to distribute it evenly. Scatter the fresh dill on top, patting it down, and cover the salmon with plastic wrap. Place a flat-bottomed container the size of the salmon (such as another baking dish or baking sheet) on top of the salmon, and weight it with a heavy object such as an iron skillet, bricks, or a few cans. Refrigerate the salmon for 24 hours, flipping it occasionally to ensure even curing and redistributing the cure as necessary. As the salmon cures, its moisture is drawn out to produce a brine. Remove the plastic and check the salmon for firmness. If it still feels fleshy, lay it flesh side down directly in the brine. Continue to cure for up to 12 hours, or until the thickest part of the salmon is firm.
Remove the salmon from the refrigerator and pat it dry. Set it, skin side down, on a wire rack set over a baking sheet, and allow it to air-dry in the refrigerator for an hour or two. (The cured salmon can be wrapped tightly in plastic wrap or parchment paper and stored in the refrigerator for up to 2 weeks.)
Slice the salmon as thin as possible with a very sharp knife, and serve with the Mini Potato Pancakes and Chive Sour Cream. Alternatively, sliced salmon may be diced (skin removed beforehand) and served with traditional garnishes tartare-fashion (boiled eggs, red onion, capers, toast points, and an herb oil).