Put morels, porcinis or both in a bowl with very hot water to cover; soak until soft, about 20 minutes. Drain morels and reserve soaking liquid. Cut morels in half; if porcinis are large, chop them roughly.
Melt butter in a large skillet over medium-high heat; when butter is hot and foam has subsided, add shallots and reconstituted and fresh mushrooms to pan. Cook until shallots soften and fresh mushrooms have released their liquid and it has cooked off, about 10 minutes.
Add asparagus and 1/2 cup reserved liquid to pan. Bring liquid to a boil, cover, reduce heat so mixture simmers, and continue cooking for another 2 to 4 minutes, or until asparagus is crisp-tender. Add cream and tarragon or chervil and continue cooking, uncovered, until sauce thickens slightly and asparagus is tender, about 4 minutes more. Season with salt and pepper and serve.