Begin by preparing the asparagus. Peel the lower stalks and soak in cold water for at least 20 minutes. Rinse, then simmer in boiling water, uncovered, for 10 minutes. Drain and set aside.
Set aside 6-12 small slices of Fontina cheese for the top of the bundles. Divide the remaining cheese into 6 piles.
Spread out 1-2 slices of prosciutto. Place 3 asparagus spears inside, then one pile of Fontina and a small bit of butter.
Roll the bundle and place it into a buttered baking dish.
Repeat for the other 5 rolls.
Place the 2 thin slices of Fontina on the top of each bundle and add a small dab of butter.
Place into a 400° and bake for 20 minutes, or until the cheese has melted and a nice, golden crust has started to form on the top of the bundles.
Remove and let cool for 5-7 minutes. Spoon some of the juices on top of each bundle when serving.