Preheat oven to 375 degrees.
In a skillet melt half of the butter. Add onion and sauté over medium heat until golden. Add mushrooms and cook until soft. Add chicken ,salt , tarragon, and garlic. Cook until chicken is brown.
Mix in cheese, Prosciutto, and egg.
Brush 1/2 filo sheet with melted butter.
Spoon 1/3 cup chicken mixture on narrow edge and fold in sides.
Roll up and place, seam side down on a baking sheet. Repeat with remaining sheets of dough.
Brush the rolls with remaining butter. Bake for 20 minutes until golden brown.