An example turbofan engine restarting system includes a core nacelle housing, a compressor, and a turbine. The core nacelle is disposed within a fan nacelle. A bypass flowpath downstream from the turbofan is arranged between the two nacelles. A controller is programmed to manipulate the nozzle exit area of the bypass flowpath to facilitate startup of the engine. In one example, the controller manipulates the nozzle exit area using hinged flaps in response to an engine shutdown condition. The flaps open and close to adjust the nozzle exit area and the associated bypass flow rate, the mass flow rate of the air through the core nacelle and the rotational speed of the compressor rotor.