The Drama Desk Awards, one of Gotham’s annual legit kudofests, is getting a makeover — again — tapping Joey Parnes Prods. to produce and general manage the June ceremony.The 57-year-old awards, held for in an auditorium at Gotham’s arts-centric La Guardia High, last year moved from Sunday to Monday night and was held at Hammerstein Ballroom. The evening didn’t run smoothly, provoking grumbling. This year TheaterMania.com will present the ceremony at midtown’s Town Hall with Robert R. Blume and David S. Stone, in association with Renee McCurry. It’s be the first time the legit-oriented website will take an active role in presenting the event. Parnes, who for eight years was the coordinating producer of the Tony Awards, recently launched his own shingle following a short stint as exec director of Off Broadway Public Theater. Drama Desks honor both Broadway and Off Broadway work. Nominees are named by a committee of journos and other industry types. Ceremony reverts to Sunday night this year, landing on the sked June 3, a week ahead of the Tony Awards. Noms will be announced later in the spring.