Maybe the first was as a senior. I got Kelley, General Topology and once a week gave a lecture to a prof! One week a chapter, and the next some exercises! It was fun!

The next time was on a written qualifying exam: The exam had an error, and I wasted time trying to prove it! I asked for an oral. One guy tried to haze me, but the other profs were nice, and I walked out with a rare "High Pass".

The third time was for my oral defense of my Ph.D. dissertation.

I was out running, and when I got back my wife said I'd gotten a phone call from a prof, the Chair of the committee that was to approve my dissertation -- no pushover, the Chair and a majority of the committee had to be from outside my department. Well, the Chair called me. Still with sweat from running, on my back on the bed, I had the actual oral exam! He had a question about one paragraph, so I reworded it, had my word processing retype the thing, and he was happy.

Then the fourth oral exam was the dissertation defense -- it was for show since the real one had been over the phone. The Chair looked really serious and let me look really serious and good.

Maybe there was one more: I'd rushed ahead in freshman calculus and done the first year on my own. Then I asked to start on sophomore calculus and never take freshman calculus. So, the prof gave me in effect an oral exam on freshman calculus. He concluded I'd passed and let me in sophomore calculus. He did say that he couldn't give me course credit for freshman calculus, but fine with me -- I just wanted to get going, get on with calculus, and not repeat what I'd just studied well.

https://www.math.princeton.edu/graduate

Generals/Quals require 1-2years of graduate level study, not remedial undergrad, if you look at the material covered and the syllabus and levels assigned to courses at various colleges. It just so happens that at a school like Princeton, 1st year PhD students have already taken graduate level classes in their field, or equivalent self study.