Help Me Name My Mystery Vegetable!

 Do you know what this mystery vegetable is? I got them at a neighborhood plant swap and the name started with an "s". Something like shallots or scallions. We pulled them all up and cooked (bulb, stems and all) them in early Spring, but left two to "mature" and this is what we got.

These look like little baby mystery "s" plants that would probably fall to the ground and root eventually, do you think? Should I separate and plant them?

 

Here's the mystery plant in the garden bed.

 

..and here's the stem.  Any guesses on this plant? When do you harvest it and what parts do you eat? 

UPDATE: Mystery solved! Egyptian Walking Onion! Thank you Kathy!

Loretta

p.s. I'm still interested in your opinions on my which of my three Master Plans I drew up for my house is your favorite! Click here to see them. Thanks!