Between May 5 and July 4 there are six or more first class award seats available most dates from Miami to Milan on American Airlines.
This makes sense. American has made first class award space available in the months leading up to a change of aircraft away from an old configuration Boeing 777-200 (which offers first class) to either a reconfigured plane or another aircraft type with no first class cabin. American is switching this flight from a 777-200 to a Boeing 767-300.