It's marvellous what you can find on the internet!

Here is a link that might be useful: japanese parsley

To me, it looks like Cilantro..

Not cilantro. It has a flavor that is, well......mitsuba to me. Doesn't taste like normal parsley to me.

I've tried direct sowing and starting inside and have had better germination with indoor starts, unlike normal parsley which I usually start in situ.

I have a hard time getting size on the plants but I suspect that I need to try a different location. It just isn't happy with the vegetable bed conditions. I'm going to try a cooler location, part sun and see if it likes that a little better.

Here is another source for it from one of my favorite places.

FataMorgana

Here is a link that might be useful: Nichols Garden Nursery - Mitsuba

I love this plant. But: it can become extremely invasive. I have the bronze leaved type and it grown through the lawn, etc. It grows well in both sun and shade. I don't think it has much flavor, but I sometimes use it to decorate platters, etc.
I think this is the same as what I have Cryptotaenia japonica atropurpurea.
The plant is lovely until it flowers. The flowers are the least attractive kind of flowers, no petals, just little branches. Then all of a sudden the seedings are everywhere, I mean everywhere.

What I do now, is every time a plant gets going and looks like it is thinking about flowering, out it comes. It feels harsh, but there are so many seeds all over my garden, it keeps coming back.

Another nice thing about this plant is that Swallowtail Butterfly cats love to eat it. Being easy and quick to grow is a huge plus over regular parsley as the cats eat a lot.