The Boston Planning & Development Agency (BPDA) Board of Directors approved a residential development project in South Boston near Broadway Station.   The 21-35 West Second Street will construct a new six-story building with 55 residential rental units, approximately 2,600 square feet of ground-floor retail space, and two on-site parking spaces for car share services. Seven of the residential units will be income-restricted. The project is located in proximity to the Broadway MBTA Station, which provides residents with access to the 9, 11, and 47 bus routes as well as the Red Line. Residents of the building will be ineligible for Resident Permit Parking.  The project will include 1,600 square feet of additional outdoor seating, public space, street lighting, and associated streetscape improvements, and will add sidewalks around the perimeter of the site. The developer will contribute $15,000 for the study, design and implementation of on-street parking improvements.