A project to resurface nearly 15 miles of Montauk Highway between East Hampton Village and Montauk is set to begin on Sept. 29. Eileen W. Peters, a spokeswoman for the New York State Department of Transportation, said the project is separate from but similar to one completed before Memorial Day in which 8.2 miles of the highway were repaved between County Road 39 in Southampton and Stephen Hand’s Path in East Hampton.