Italian carrier Meridiana is offering some great option from Milan either to Recife or Fortaleza in Brazil. (However Air Malta as a subsidiary of this carrier operates these flights). Very limited seats are available though. Round trip flights on said routes are now starting at just €362! All charges and checked luggage are included. This includes some options to fly to Brazil over Christmas holidays or NYE.
Meridiana offer is valid for flights in travel period from October 2016 till April 2017. You may check travel dates directly with the carrier. In general look for flights departing / arriving on Thursday.
Booking sample of cheap direct flights from Italy to Brazil from €362! In this case you would depart from Milan to Recife on 29th of December 2016. Your return flight from South America back to Europe would be on 5th of January 2017. Great opportunity to celebrate NYE out of EU in some exotic holiday destination..