DA-42 instructor pilot reported safely returning to departure airport after the left engine would not restart following shutdown for a training scenario.

Narrative

Left hand engine would not restart in the air. After engine shutdown in flight maneuver done by student pilot; the engine started windmilling slightly. Instructor lowered airspeed to 85 kts. and the windmilling stopped so we attempted a start. Engine would not start but was in the unfeathered position. Student did all the right steps to turn the engine back on; we got the starter to crank momentarily and then the propeller stopped again. Instructor took controls at this point and decided to turn the engine master off again; the propeller was still in the unfeathered position. We attempted to restart in the unfeathered position but the starter would not engage this time so we secured the engine and made a landing back at ZZZ. While we were troubleshooting; instructor started flying towards ZZZ and called ZZZ Tower to [advise ATC]. After securing the engine; heavy windmilling occurred on the way back to ZZZ; even at lower airspeeds. We made a safe landing and were able to roll off the runway with one engine. Windmilling stopped after we got on the ground and we restarted the engine on the ground after crossing the hold short line and taxied back.