Cook the asparagus in a large pot of boiling salted water until it is tender, but not soggy, about 3 minutes.
Using a slotted spoon, remove the asparagus, then use the same water to cook the pasta. The pasta should be tender but still firm.
Drain the pasta and return the pasta and asparagus to the same pot.
In a large skillet, melt the butter over low heat. Add the garlic and tarragon and stir 1 minute.
Add the morels and sauté 4 minutes.
Add the cream and broth, boil until the Morels are tender and the sauce thickens slightly, about 4 minutes.
Stir in the cheese.
Add the sauce to the pasta and asparagus, tossing to coat. Season with sea salt & freshly ground black pepper to taste.