Divide the salmon fillet into two equal pieces. Dry. Season with salt and pepper.
Heat 2 teaspoons of olive oil in a skillet over high heat. Arrange fillets with the outside side up, cook until golden brown, about 5 minutes. Then turn over, reduce heat to medium, cook for 3-5 minutes. Transfer to a plate, cover with foil.
Empty the pan. Put butter and 1 teaspoon of olive oil on it. Put half of the asparagus in the pan with the tips in one direction and half in the other. Sprinkle 1/8 teaspoon salt on the asparagus and stir in gently.
Cover and cook for about 5 minutes. Remove the lid, add heat, and continue cooking until soft and golden brown.
Chop the onion and parsley finely. Beat the remaining butter with lemon juice, onion, parsley and mustard, season with salt and pepper.
Transfer the asparagus to the salmon, pour the dressing over the dish.