In the case of every appeal made to the Board of Appeals, every application for a special permit and every petition for a variance to said Board under the provisions of this chapter, the Board shall hold a public hearing thereon. Notice of the hearing shall be given by publication in a newspaper of general circulation in the Town once in each of two successive weeks, the first publication to be not less than 14 days before the day of the hearing. Notice shall be sent by mail, postage prepaid, to the parties in interest, including the petitioner, abutters, owners of land directly opposite on any public or private street or way and abutters to the abutters within 300 feet of the property line of the petitioner, including land in another municipality, as they appear on the most recent applicable tax lists, the Planning Board and the Planning Board of every abutting municipality.