Preheat the oven to 400 degrees F.
Bring 6 quarts water to a rolling boil and add 2 tablespoons salt.
In a 12-inch saucepan, heat the butter over a medium flame until it foams. Add the veal and the prosciutto and cook until golden brown, about 5 to 7 minutes. Set aside.
Peel the onions and carefully drop in the boiling water. Cook until the onions are tender but still retain their shape, about 25 to 30 minutes. Drain the onions and set aside to cool.
Once the onions are cool enough to handle, cut them in half cross-wise, and carefully remove the very center from each half of the onion. This will create pocket for the stuffing. Repeat with remaining onions.
Crack 1 egg, and, using a wooden spoon, mix the egg into the cooled meat mixture. Salt and pepper, to taste, add 3 tablespoons Parmigiano and a pinch of nutmeg and mix until well combined.
Lightly grease a 13-inch baking dish. Use a spoon to gently spread meat mixture on top of each onion half. Place the stuffed onions, stuffing side up, into the prepared pan. Drizzle the grappa over the onion halves. Sprinkle the onions with the crushed cookie and crushed breadsticks. Sprinkle with the remaining Parmigiano. Place in the oven and bake until the cheese is golden brown and bubbly, about 45 minutes.
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