Our first member of the poppy family is Eomecon chionanthum, commonly called Snow Poppy or Dawn Poppy, though I first knew it as Chinese Bloodroot. This perennial spreads by long reaching underground stolons, which ooze orange/red sap when broken or cut. (Note: wear gloves when working with this plant because, despite the lovely color of the sap, I found out the hard way that it is difficult to remove the color from your hands for a day or so.)
Each leaf has its own petiole and all petioles come up separately from the ground. Blooms are on their own stems, all of which are quite smooth and hairless (quite un-poppylike) and grey green. The flowers are white with yellow centers and are and inch to an inch and a half across. They seem to face the ground when they are first opening up, but face outwards once they are fully open.
A small warning: This one will spread, coming up in all sorts of places, but it is lovely and easily pulled out, roots and all, so keeping it in check is just a matter of a bit of weeding occasionally. Just watch where you plant it and keep up with the weeding and it is really a lovely thing, especially when it is in bloom.
Main flowering season is May and June, but I often see the occasional bloom in summer or fall. Ours seem happy in light shade, even with some afternoon sun. They will grow in colder climates, but will be gone for the year with the first frosts and are a bit late to return in the spring, which is probably for the best since they are so frost sensitive.
Eomecon can be propagated from seed, but it is much easier to just lift some of the 'extra' plants you're sure to have and transplant them. Expect them to wilt for at least a week after you transplant them or pot them up. It's just something they do. Keep them watered well and soon enough they will be back to normal.
There are people who would say you shouldn't grow this one, but with only a little 'neatening' a couple of times a year, it will grow happily and provide a lovely addition to your garden.