In a food processor, pulse together the salt, sugar, dill, lemon zest, and black pepper until you have a coarse mixture.
Lay a large sheet of cling film on your work surface and spread half of the cure mixture on it.
Place the salmon skin-side down on the cure and cover the top completely with the remaining mixture.
Wrap the salmon tightly in the cling film and place it in a dish or tray.
Refrigerate for 2–3 days, turning once a day if possible.
Once cured, unwrap the salmon and rinse it thoroughly under cold running water to remove the cure.
Pat dry and slice thinly at an angle.
