Wash the asparagus, peel the lower third and cut off the ends. Cut the asparagus diagonally into slices about 1 cm thick. Cook in little boiling salted water for 6-8 minutes. Clean the shiitake, cut off the stems and cut the mushroom heads in half or quarters, depending on their size.
Wash spinach thoroughly, sort and drain. Chop the walnut kernels. Mix vinegar with a little salt and pepper, then fold in the oils. Add the walnuts. Drain the asparagus on a sieve.
Heat the fat in a pan and fry the mushrooms in it until golden brown. Season with a little salt and pepper. Mix asparagus, spinach and shiitake and arrange on plates. Spread vinaigrette over them.