Place broth, water, potato, shallot, garlic, thyme, savory (or marjoram) and salt in a large saucepan. Bring to a boil over high heat. Reduce heat to medium-low, cover, and simmer until the potato is tender, about 8 minutes. Add asparagus, return to a simmer, and cook, covered, until the asparagus is tender, about 5 minutes more.
Meanwhile, cook prosciutto in a small skillet over medium heat, stirring, until crisp, about 5 minutes.
Pour the soup into a large blender or food processor (see Tip); puree until smooth, scraping down the sides if necessary. Season with pepper. Serve topped with the crisped prosciutto.