Hi dshell,
You are off to a good start for next year's leeks, by seeing your uneaten leeks go to seed! I do this almost every year - BUT, i dry and collect that seed for late winter or early spring sowing. I take the almost dried flower with black seed showing, and remove it to continue drying where i can catch the seed and give it a gentler start in containers of moist soiless seed starting mix. Because the mix is clean and holde moisture while germination happens, i can plant out my leek babies when they are stronger and the climate is right. Seedlings from alliums seem to do better with a light, fluffy growing mix - rather than our clayish soil outdoors. Altho i start alot of different kinds of seed every year, once my alliums are up, i can move them away from the lights and just into a cool or cold windowsill in the basement. I give them occasional haircuts if they get a bit floppy, and they are fine with it until i can get them into the ground in early spring. Leeks are the first seed i sow indoors for the year - late January or early Feb. here in zone 6. I always let around 4 -8 of our leeks go for fresh seed.......and the blooms are nice to look at!
Good Luck,
Glad

Thanks for the answer, but I am really slow. Do I start the little green shoots or plant the seeds? Is it necessary to start them indoors? In order to eat them, do they need to be picked before they form a seed pod?

Thanks!