Thrice or triple?

Pretend it would concern the number two instead of three:

Use thrice when you would use twice.
Use triple when you would use double.

As they have been cooked three times, I would suggest "thrice".
For comparison: I have seen you triple today. Doesn't work, does it?

If it is a fairly well-known recipe, then the name is a fixed phrase by now — and also, well, a name. So it cannot be wrong by definition. It's a label, and as far as the English language is concerned, it can be anything at all. You might as well wonder if New York should be called Second York instead. Or Little Pear. It should nothing. It just is.

Thrice is rather old fashioned these days, even archaic. It's valid, but 'triple' conveys the meaning perfectly adequately.