Combine the salt, sugar, cracked black pepper and vodka 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 sprigs on top, patting them 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 until the thickest part of the salmon is mostly firm to the touch, 12 to 16 hours longer.

Remove the salmon from the refrigerator and pat it dry. Set it, skin side down, onto 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 thinly as possible with a very sharp knife, cutting the slices away from the skin and trimming any of the dark bloodline away before serving. Serve the slices with the Mustard Sauce and toast points or crispbread.