To vary or modify the application of the requirements or provisions of the Town or village zoning code, including the grant or denial of specific types of variances set forth in the respective zoning codes, which requirements or provisions have caused a denial of a permit, certificate or other form of approval by the Code Enforcement Officer of the respective municipality. Such application for a variance shall be heard and decided in accordance with applicable procedures set forth herein and by the laws of the State of New York, as may be amended.