Into a flameproof casserole dish which the chicken fits tightly, put the chicken. Pour in enough stock to almost cover legs. Cover chicken breast with a sheet of buttered waxed paper. Cover and simmer 1 hour, or until chicken is just cooked. Remove chicken from casserole dish and cool.
Add onions and milk to stock. Boil rapidly uncovered, until liquid is reduced to 1-1/4 cups of thick pulpy onion sauce. Preheat oven to 350F (175C).
Remove skin from chicken. Cut meat into small pieces and place in a large bowl. Add onion sauce, half the butter, the lemon juice, cheese, salt, pepper, nutmeg, parsley and eggs. Mix well together.
Lightly butter roasting pan. Brush 1 sheet of dough with butter and place in pan, overlapping edges. Brush 5 more sheets of dough with butter and layer them on top.
Spread the filling over the dough. Flap overlapping dough over top. Cut remaining sheets of dough to fit pan. Brush with butter and layer on top. Score top into squares and tinkle with water. Bake 45 minutes, or until golden-brown and crisp. Serve with salad greens.