Construction has begun on a new medical office development in Patchogue .  The $10 million project will bring a two-story, 12,000-square-foot building to a .84-acre parcel of vacant land at 60 Lake St. at the western entrance to the Village of Patchogue.  The developer of the office project is Avgi LLC, an entity headed by Allon Avgi.  “It’s the first thing you see when you come into the village and we wanted to make it as beautiful as possible for that vacant site,” Avgi to