Reconstitute morels, taking care to reserve the liquid.
Cut the mushrooms lengthwise into halves or quarters depending on the size of the mushrooms. Pat dry and set aside.
Steam the chopped asparagus for three or four minutes, or until barely tender when pierced. Set aside.
Stir the pine nuts in a large skillet over medium-low heat until lightly browned. Remove the nuts from the pan and reserve.
Melt the butter and add the morels and shallots, stirring often. Sauté for four or five minutes until the mushrooms are lightly browned.
Add 1/2 cup of the reserved morel soaking liquid and the cream. Bring to a boil, stirring frequently, until the liquid is reduced by about a third.
Prepare the pasta according to package instructions.
Add the chive leaves, the thyme, and the asparagus to the sauce. Cook until heated through. Season to taste with the salt.
Top the pasta with the sauce, sprinkle with the pine nuts, and use the chive blossoms for a garnish. Serve with Parmesano.