Wash the asparagus, cut off the woody lower ends. Peel white asparagus and cut into thin slices at an angle. Put them in boiling salted water with 1 pinch of sugar, bring to the boil and cook for about 1 minute.
Pour into a sieve and drain well. Peel onion and chop very finely. Mix vinegar, onion, pepper and 1/2 teaspoon sugar. Fold in the oil. Mix asparagus and vinaigrette. Clean the mushrooms and slice them into thin slices.
Wash the mussel flesh and dab dry. Melt butter in a pan, add mussels and fry briefly on each side over medium heat (butter must not brown). Season with salt and pepper.
Place two mussels in a mussel shell, spread mushrooms on each, sprinkle with cheese and drizzle frying fat over them. Grill in a preheated oven for 2-3 minutes. In the meantime wash the tomatoes, cut them into quarters, remove seeds and dice the flesh very finely.
1 minute before the end of the grilling time, carefully sprinkle the tomatoes on the mussels. Garnish asparagus and mussels with chervil.