Notice of the hearing shall be given by publication in the official paper of the Village of Dering Harbor one time not less than 10 days before the date of the hearing, and by requiring the applicant to mail written notice of the date, time and place of the hearing, and a summary of the purpose of the application submitted to the Board, by certified mail, return receipt requested, to every property owner, as shown on the current Village of Dering Harbor assessment rolls, of parcels within 250 feet of the property which is the subject of the application, proof of which shall be submitted to the Board on or before the commencement of the public hearing in the form of an affidavit with postal receipts annexed thereto confirming mailing of said notices at least 10 days prior to the hearing date. The failure of the notice to be published in the newspaper or the applicant to provide the required proof of mailing shall require the Board to adjourn the public hearing and cause the public hearing to be renoticed.