MK6 2014 GTI suddenly stalled, wouldn't restart

FINAL UPDATE: It's been a week and 500 miles and no further issues. I don't like this kind of problem that seemingly solves itself. I don't like worrying that my car is going to leave me stranded. Thanks for everyone's help and suggestions.

UPDATE #2: No further problems since this happened 2 days ago. I scanned for error codes and none were found. Yesterday I put in a bottle of Sea Foam with a fresh tank of fuel and then drove it hard for a while. All seems fine.

FYI - I paid $11.99 for a 16 oz bottle of Sea Foam at AutoZone, but I see that it's only $6.99 at my local Target.

UPDATE #1: Thanks for the suggestions and links. I drove the car several times later yesterday and now this morning. No recurrence of the issue.

Per several suggestions in other threads I did an Italian tune up (which I had to look up...), which is a very different type of driving than is typical for me, which raises a question:

I baby my car and drive it more for mileage and longevity than flying around at high RPMs as many GTI owners do. For me to take it out and drive at 4-7k RPM is WAY more aggressive than I usually drive. Is it possible that my low RPM 36k miles have led to carbon build up being a more likely culprit?

Also, if it's the HPFP as several people suggest, would that be out of warranty since my car is now almost 4 years old?

Original: My 2014 has 36k miles on it, has been regularly serviced, and has had no issues since new.

I returned to my car in a store parking lot today after about 15 minutes inside. To this point the car had been operating perfectly all day (and ever since I purchased it new). It started up, then sputtered and died about 30 seconds later while driving in the parking lot. It restarted immediately, ran for about 5 seconds, then died again. Several more attempts to restart would result in a maybe 1 second of rough engine, then dead.

After about 45 minutes I gave it one final try and it started right up, idled evenly, and I drove home with no further issues.

There were never any CEL or other idiot lights before, during, or after these issues. I had a half-full tank of gas, and it's a DSG. I did not stop anywhere to pull codes.

Any thoughts on what might have happened, and if I can do anything other than wait for it to happen again? Thanks.