Toss the bread cubes with four tablespoons of melted butter and spread the mixture on three baking sheets. Sprinkle the mixture with the Parmesan cheese and bake about 15 minutes before returning the bread to the bowl.
Melt remaining butter in a skillet before adding the onion, scallions and celery. Cook over low heat for 10 minutes.
Add the prosciutto and cook over medium heat for five minutes before adding the apples and thyme. Toss the mixture with the bread cubes, add salt and pepper to taste.
Whisk the chicken stock and eggs together in a bowl. Pour the mixture over your stuffing and stir well.
Divide the stuffing onto as many baking dishes as needed and cook it under foil for about 30 minutes.
Uncover the stuffing and cook it for an additional 10 minutes until browned.