Bonanza 35 pilot reported engine failure on takeoff. The pilot restarted the engine and taxied off the runway to trouble shoot the engine problem.

Narrative

Aircraft was at ZZZ for maintenance (biennial pitot/static/transponder check.) Flight purpose was three night take off and landings (full stop) at ZZZ; then continue to home base about 35 NM south east ZZZ1; three night take off and landings there. Completed POH pre-flight and pre-takeoff checks at base. Fuel was about 25 gallons each tank. As I conducted the pre-flight; the pattern was empty; as I completed the pre-takeoff checks; several aircraft were entering Class D. Called Ground; asked for taxi to Runway XX; three takeoff and landings in the ZZZ pattern; then departure to the south-east landing; ZZZ1. Got clearance to taxi; waited a bit then got takeoff clearance. No issues during takeoff; climb left crosswind; downwind base. Landing was uneventful; came to a full stop with throttle out; mixture and prop in. Pushed the prop full forward; and the engine kept turning but made no power; not even enough to taxi. There was traffic behind me to the same runway. Advised Tower that I had an engine failure on the active runway and to standby. Tower replied and advised traffic behind me. Confirmed prop; mixture; throttle forward. Moving throttle had no effect. After several tries; the engine quit completely. Was able to restart after pulling the mixture out about half an inch. Requested departure from Runway XX; left on Taxiway X back to mechanic to troubleshoot. Mechanic went through the entire engine start procedure three times. Tried to simulate the engine stoppage. Was not able to. At this point everything was working normally. Decision point was whether to leave the airplane at ZZZ for the night; or continue to home base. Came to the conclusion to abandon the departure airport pattern work; takeoff; carefully watch the engine during ground roll; be primed to abort and then climb to a higher altitude that is called for this trip. The area is farmland between the two airports with a ridge across the track but fields available the entire way. Called Ground back and requested departure back to ZZZ1. Got taxi clearance then takeoff clearance; right on course and climbed to 3500 ft. MSL direct. Kept altitude until approach into ZZZ1. Kept the final to Runway XX high with low power. Landed. No issues with the engine. Taxied back to Runway XX. Completed another three takeoff and landings with no incident. Reviewed incident and my actions the next day with a flight instructor/A&P mechanic at home base. Obvious questions were did I miss something? I don't think so. Did I have power out on a long final. I did. This led me to wonder whether the idle was set correctly on the aircraft. If not; it may have led to partial flooding on final which contributed to the engine stop when operating the throttle. Sent the aircraft to the local shop; squawked 'engine failure on the go.' Mechanic was able to reproduce the stop. Found that the idle setting was too low. This was corrected.