No wonder the breaker did not trip. 1000 seconds is 15 minutes and change. The elements start cycling off after 10 minutes.

To answer CDN, no the elements are good. I pretty much took this whole thing apart to figure it out. This was a replacement grill that was bigger than the first one and nobody bothered to upsize the feed.

As for the 3 breakers vs 2 breakers, its not an overcurrent problem as much as a disconnect problem. If one element shorts it will only disconnect 2 of the 3 phases. Or someone unaware of this is working on the grill may not know to disconnect all of them. Somewhere in the code it states that all 3 phases must be disconnected at the same time. I should add that the breakers are the disconnecting means.

I guess UL has decided that having #10 wire at 37 amps for 15 minutes will not hurt it, other wise why would they list a breaker that could do that?

More breaker stories:

Had a problem with a square D breaker tripping. It was a 20 A single pole, turns out that there was a lift station pump on the light circuit and the combined amps was 25 (12 plus 13) and it would trip if the pump ran for more than 5 minutes.

Another time we had 6 - 20 amp lighting breakers pulling 18 to 19 amps. They were grouped together. Would start tripping at 10:00. Two hours after the place opened.

Yet another time had a kitchen exhaust fan on a 3 phase 20 amp breaker trip after 55 to 60 seconds every time it was started. Problem was shorted winding to ground and it pulled 40 amps. This was GE brand.