Make sauce by combining green onions, mayonnaise, lemon juice, garlic cloves and tarragon. Set aside.
Brush one sheet of phyllo with butter.
Place one chicken breast in one corner.
Spoon on the sauce.
Top with slice of cheese.
Roll over the phyllo sheet placing the fold inside.
Brush with melted butter.
Sprinkle with parmesan cheese.
Bake for 1 hour in a preheated 350°F oven.
Tip: Notes Remove phyllo from freezer night before. When ready to prepare, take out 6 sheets and return package of phyllo to freezer. Place you phyllo between damp sheets of paper towels. Cover with tea towel to keep them damp, otherwise they will dry up and become brittle.