Place the salmon, skin side down on a plate. Cover the top with a combination of the coarse salt, sugar, white pepper, and chopped dill. Cover the plate with plastic film and place a weight on top. Refrigerate for 2 days.
Rinse the salmon to remove the salt coating. Dry with absorbent paper. Cut the salmon into very thin slices.
Whisk the mustard, sugar, and vinegar together. Slowly whisk in the oil, drop by drop, to make a mayonnaise. Add the minced dill and season with the salt and pepper.
Arrange the salmon slices on chilled serving plates. Serve with the mustard sauce.