Wow, French Fries, I'm really glad you made this dish. I keep telling people about it, but people keep ignoring the recipe because nobody seems to like cauliflower. Everyone thinks, i'm sure, "oh, that boiling cauliflower smell" and don't want to try. But the flavor is entirely different from boiled cauliflower, and the sweetness of it comes out wonderfully. You can do a similar thing with zucchine, but it's not nearly as tasty - zucchine being pretty tasteless. But it totally transforms the cauliflower.
I usually use rigatoni, because i feel it needs the bite of a thick pasta. I particularly dislike farfalle, because they are always undercooked where the dough is pinched together, or overcooked on the flat parts. But i like the bite of rigatoni.
I always put a good amount of parmigiano on the pasta as soon as it's drained, so it sort of melts on (don't mix yet, because it will cling to the spoon and bowl. Then I put the cauliflower on top, and then mix well.
I usually like vegetables al dente, but in this case i like the cauliflower to get soft completely through. It doesn't really fall apart, Koukouvagia, at least not entirely, though there will be tiny flower buds like little grains at the bottom of the pan, which spread the flavor throughout the dish, but it should get soft, i think, but it's up to you. I probably would have cut the bigger flowers in half or in quarters (lenghthwise up the stem and flower) and they cook faster.
It doesn't need to be very oily, as long as you keep an eye on it and keep it covered so a little steam adds to the liquid.
I tried it once with broccoli but it didn;t work right.
With broccoli, instead, I like to blanch it, and then get the frying pan with a good film of oil, add cubed pancetta and garlic and optional red pepper flakes or whole hot peppers, cook very slowly till pancetta is lightly browned and the garlic is soft, then keep cooking a few minutes with the broccoli in it, and then dump it on the pasta and cheese.