At least on my farm, leeks are easy to grow. I've never tried growing them from seed, instead, I buy plants from Dixondale. A bundle of baby plants is reasonable enough. The variety I get is called Lancelot. It does very well here. I'm aware that there are lots of other varieties, but I don't know which ones do well with short days. Thus so far, I've stuck with Lancelot.
Up till now I haven't done much experimenting on how to grow leeks. The appear to like my loose, fertile soil well enough. And they really respond well to compost tea. Keeping them mulched causes them to grow vigorously. If I build the mulch up or pull soil up against the leeks as they are growing, I get a longer shank. Basically I pull the mulch around them then top it with a bit of soil, then add a bit more mulch. Do that every two weeks or so and the leeks grow well. Well, that's the way I grew them last year. This year I only had a handful of leeks in the community garden and we never got around to doing anything with them. But they still grew great but had shorter shanks without having been thickly mulched. So one can get leeks without mounding up the soil or mulch, but the length of shank suffers. Flavor is still marvelous.
I read in the Nichols email newsletter that if you planted the cut off root piece, it would grow another leek. I took that idea and modified it. When I harvest leeks I pull the mulch and soil away then cut the leek about 1" above the roots. The leek rapidly regrows. Wow! Just the kind of veggie my garden likes, cut 'n come again!
The photo below is where a leek was harvested in the morning. By late afternoon I could see the central core had grown half an inch already.