I'd like to try that! Do you remember what it was called?

There is the "Rubik's Impossible"

https://www.rubiks.com/products/rubiks-impossible

Sticker sets are also available, like this one

https://oliverstickers.com/two-face-3x3x3.html

I'm not a cuber or a puzzle guy or a math guy, but I am curious: how do you know when it's solved? Or is this a 'whoosh' moment and I'm missing the obvious?

when it's solved you look at all blocks on a face from the same angle, so they all have the same color. the problem is, while you are solving you don't know from which angle you need look at one block. you see a red one on one face, and another red one on another, and when you bring them together you realize that you looked at one of them from the wrong angle and they don't actually match. so effectively you need more moves until you find the right block.