Combine the sugar, kosher salt, and pepper corns in a small bowl and mix well. Do not use table salt. We recommend Diamond Crystal Kosher Salt or Morton's.
Place the salmon in a shallow dish and rub a handful of the salt mixture into both sides of the fish. Sprinkle the salmon with the remaining mixture and cover with the dill. Cover the dish and let it cure for 36 hours. Turn it over every 12 hours. If you are curing a whole side of salmon, the tail part will cure faster and can be remove earlier.
Gather ingredients for the mustard sauce.
On the day of serving, prep the mustard sauce by combining the mustards, sugar, vinegar, coffee, salt, and pepper in a blender. With the machine running, add the oil in a slow, steady stream, blending until the sauce is thick and creamy. Transfer the sauce to a bowl and stir in the dill. Make this a couple of hours ahead so the flavor will come together.
To serve, using a knife and scrape the seasonings off the gravlax. Slice the gravlax against the grain and remove it from the skin. Serve with crackers, the mustard sauce and garnish with fresh dill.