Have a saucepan of salted water at a boil.
Place the asparagus in the water and blanch until just fork tender, yet still firm, 4 - 6 minutes.
In a skillet, melt the butter over medium-high heat. Add the mushrooms, and sauté until soft and they start to give off their liquid, about 4 minutes. Add the garlic and cook for 1 minute. Remove from the heat and stir in the tarragon.
Remove the asparagus from the water and dry on paper towels. Wrap one or two asparagus stalks with a thin prosciutto slice and set aside.
Place on a serving platter and spoon the warm mushrooms over the top. Serve.
Yield: 4 servings