Finally, an assigned recipe. :)
I'd never heard of this pastry before: it's a puff pastry relative with fewer turns and sugar incorporated into the last turn to make it sweet and add crunch. Years ago I made puff pastry (croissants) just to say I'd done it once, but I've forgotten any techniques I might have gained then. This was essentially a new effort for me. TL;DR: I was not so successful at it.
Making the dough was straightforward. I thought the shaping of the butter block from my high-butterfat content (Organic Valley European Style Cultured Butter) was as well, but in retrospect perhaps I should have thoroughly kneaded the butter then re-chilled it if necessary to get it to temp. I did a pretty minimal kneading mostly to get the right sized block, then checked the temperature to be sure I was in range. Alas, in the second turn I could see that my butter wasn't in a smooth layer, but was in little shingles under the dough. The obvious issue was the butter and dough not rolling out together, but exactly what I did wrong is less clear--maybe the temperature of one component was off (I checked the butter but not the dough), maybe the butter needed kneading to gain plasticity, maybe my rolling technique needs work.
I didn't see a way to fix the shingled butter at that point in the process, so I went ahead with cutting and shaping the pastries, let them rise in English muffin rings, and baked them. I got a pool of butter on the baking sheet which is probably in part due to blobs of butter melting out of the pastries. It was actually only about 2-3 tablespoons, but I suspect if the dough had layered properly there would have been less.
We tried one of these warm from the oven as Rose suggested, and even though it wasn't as well layered as I'd have liked, the flavor was good. The sugar-limiting folks next door found it on the edge of too sweet, and thought the 1/5 of a kouign amann we each got from the sample was plenty. The rest were frozen and brought out for Thanksgiving breakfast, where older brother's family (much less sugar-averse) thought they were wonderful.