Thanks for the explanation, OldSchool.
I'm familiar with top-setting onions, but not by that name. There are two common types of walking onions; the Egyption Walking and the Catawissa. Superficially they are the same, but there are differences. For instance, the Egyption Walking onion does set an underground bulb, whereas the Catawissa doesn't.
The term "walking" refers to the fact that if left alone the weight of the bulbils causes the leaves to bend down to ground level, where the bulbils sprout and a new plant grows. Thus, the plant "walks." And if you're not careful it can be very invasive and take over the place. I tore out a bed for that reason. I'd started with something like 11 bulbils, and before I knew it they covered an area about 7 foot square.
Pickling the bulbils goes back to colonial days.
With one exception, walking onions are the first garden plants to green up in the spring, and are often prized for that reason alone. Another allium, the multiplier called "potato onion" (aka, hill onion, Kentucky hill onion, and a couple of others) greens up slightly earlier.
If you like the walking onions you might want to start a bed of Rakkyo; a Japanese perennial allium. Most of the bottled pearl onions you see are actually Rakkyo. One of the things that makes them fun is that, after a short summer dormancy, they start growing again in August. The set flowers in October, then go through a winter dormancy, and the process starts over. Bulbs are harvested in July.
Another fun allium is perlschwieble. With this multiplier the tiny bulbs (ranging from the size of pearl onions to pinheads) grow underground in a vertical bunch---sort of the way Brussels sprouts perform. Another possibly invasive one, because, try as you might, you never get all the pearls. But these, at least, can be contained to one area.
