Those look like elephant garlic to me, not leeks. Although technically elephant garlic is a bulbing type of leek.

Do the bulbs have individual cloves or does it have rings like an onion? If they have cloves, they're elephant garlic. If they have rings, they're leeks.

Rodney

Garlics. Cannot say whether elephant or not.

Non-bulbing varieties such as American Flag leek do not bulb up no matter how long you let them grow. I've even overwintered some varieties and they do not form bulbs. I'm not sure what you have, but it is not any of the traditional leeks. I think the above ID and suggestions are good ones.

Yours look like they grew well and should give you some good eating, though.

A simple way to know is by tasting. Leek has a mild onion taste, nothing like garlic at all. Another thing is that leek does not bulb. Its stem is its bulb. Some time it grows small bulbils to divide and multiply. But they are tiny, as I recall.

Yeah, definitely -- you have garlic, NOT leeks!!
Can't tell for sure, but I think they may be a hardneck variety (do/did they have a curling stem rising from the center and ending in a sort of flowerbud-looking thing? See link below for using these gourmet treats!).
Softneck types do not develope scapes.

Anyway, the ones you pulled are not quite mature so will not store for long; you'll want to use them up fairly soon. The rest you should leave in the ground until about half the leaves (starting from the bottom) have turned yellow &/or brown. Then pull them carefully (loosening the soil alongside with a spading fork or shovel first if necessary) and lay them out in a single layer (I like to lay mine on a screen raised a few inches off a table in my shed) in a dry, warm, dark place to "cure" for a week or 10 days. Once all the leaves have dried, cut the stalks off about 1/2-1" from the bulb, lightly rub off any remaining soil and loose outer skin, then hang in a net bag in a cool, dry place (NOT the fridge). Use within a few months.

Here is a link that might be useful: Garlic scapes

OK, I feel very silly. I didn't remember buying leeks but they looked like leeks when grown. They are probably shallots. This is also my first time to plant shallots. The reason I had gotten confused is that after I planted them, I had to move everything in one bed to another. But now after reading the remarks in the posts above and remembering better what I planted, I'm almost sure they are shallots. The ones I pulled up are very translucent, like they are water logged. That could be underdeveloped, or waterlogged since we have had non stop rain in E TN.

I planted, I'm almost sure they are shallots.
............................................

they are DEFINITELY GARLICS.
Garlics an shallots ha a major visual difference.: Shallots have tubular leaves, like onions. Garlics have flat leaves

I started off thinking it was elephant garlic as a couple of the loose bulbils looked like it, but changed my mind: I think it's actual garlic.
bibbus, do you know if garlic was planted?
It's definitely not shallots.

Bibbus, go to a grocery store with a large produce department and look at the shallots, garlic, leeks, and onions there to learn the difference.

What you have is some type of garlic. It's not leeks and certainly isn't shallots. Shallots look like miniature onions:
{{gwi:96193}}

Rodney

Rodney - those are fantastic looking shallots. It might be useful for the OP to also realise that they grow in bunches and that yours have been separated. (I assume - I have never seen a single shallot bulb growing alone)

florauk- Good point. The shallots in the previous picture were separated post-harvest. And thanks for the compliment but that picture is from a couple years ago. They didn't get quite as big this year.

Shallots grow in clusters like this:
{{gwi:70968}}
(this picture is from earlier this year)

Rodney