For the vinaigrette, wash the potatoes and cook in boiling water for about 20 minutes. Whisk vinegar, salt, pepper, mustard and honey. Add 2 tablespoons of oil drop by drop. Peel shallot and cut into fine cubes.
Wash and clean the tomato and cut into fine cubes. Wash basil, shake dry, pluck leaves from the stalks and cut into strips, except for a little to garnish. Peel the potatoes and mash them with a fork.
Stir the prepared vegetables and basil into the vinaigrette. Wash and peel the asparagus, cut off the woody ends. Cut the asparagus in half lengthwise. Heat 2 tablespoons of oil in a pan. Fry the asparagus for about 6 minutes, turning them over.
Remove the asparagus and marinate with the vinaigrette. Wash the fish, dab dry, season with salt and pepper and turn in a little flour. Heat clarified butter in the same pan and fry fish for 5-8 minutes, turning once.
Arrange asparagus and fish on plates. Garnish with basil.