Squeeze out any excess brine from the shrimp. Ideally, the shrimp should have been strained in cheesecloth for 24 hours. They need to be as dry as possible.
Coarsely chop one-third of the shrimp and put them, and the whole shrimp, in a mixing bowl.
Add finely cut dill (must be cut with a sharp knife, not chopped) and freshly grated horseradish (grated by forcibly “punching” it on the grater to create long, nice fibers).
Squeeze some lemon over the mixture.
Add freshly ground black pepper and the mayo. The mayo can either be bought or homemade; the important thing is that it needs to be as thick as possible. The goal is a Skagen that is creamy and rich but mostly shrimp, not mayo. Start with a little mayo and add more in small increments if needed.
Mix and balance with Dijon mustard, horseradish, and lemon. It should be spicy but not overwhelming. Add salt to taste.
Skagen is best when allowed to rest for 24 hours in the fridge before serving.