Does it look like this?

I am growing garlic from the supermarket (it was an artichoke and turned into a hardneck.)

Just wanted to say that I saw one of these organs, as in photo, on a multiplier as I was pulling them out last week. Shallots know this trick, just like garlic.

It does not look like the photo. The bulblets are at the base of the bulb. It is not garlic or shallots. It looks like a white onion.

It sounds like Elephant Garlic, which is a bulb-forming leek. If so, the bulblets would be brown, and very hard - somewhat nut-like. Elephant garlic normally forms several large garlic-like cloves, but if its growth was stunted for any reason, it would form a single clove ("round") about the size you describe.

That is the only edible allium I can think of that might meet your description, Betsy, but it could also be an ornamental. Those would normally bloom in the first year, though.

It is not Elephant garlic. The bulblets are small and white. They are attached to the base of the bulb.

Going by the description alone, I would second zeedman's guess of elephant garlic...maybe a picture would help?

Hmmm... if those bulblets are roughly pea-sized, then what you have might be Pearl Onion (Allium sphaerocephalumn) a.k.a. Pearlzweibel. The central bulb will be larger; for me, they seldom exceed 1.5" in diameter. There are flower stalks on mine this year, but some years they do not bloom.