Carefully place the eggs in a medium saucepan and cover with cold water. Cover the pan and bring to a boil over medium-high heat. Allow to boil for 3-4 minutes. Keeping the pan covered, remove the egg from the heat and allow to rest in the hot water and steam for 20 minutes. Drain and rinse in cold water until lukewarm.
Meanwhile, slice the prosciutto into pieces that are 1/4″ wide and about 1/2″ long. Cook in a skillet over medium until browned and crispy.
Whisk the prosciutto into the Parmesan cheese and mayonnaise. Cover and refrigerate until ready to use.
When the eggs are cooled, carefully peel them and slice in half lengthwise. Scoop out the yolks and mash them into the mayonnaise.
Transfer the yolks to a pastry bag fitted with a large tip or a plastic bag with one corner cut out, and pipe the filling into the egg whites. Cover and refrigerate until ready to serve.