Allium cepa var. proliferum
Walking Onions are like ordinary onions, but with an entertaining (if slow) form of inter-generational vegetative locomotion. At the end of the reproductive cycle, the typical allium cepa drops seeds from its fertilized flower. The walking onion, rather, retains its seeds in the flower. The seeds germinate in place with the next rainstorm, and begin to grow into new onion bulbs right there at the top of their parent's stalk. Eventually the young onions become heavy enough to bend the stalk to the ground. Thereafter, roots are grown into the soil and the young plants continue the cycle as a successful new generation. Whether there is a slope involved or not, this tends to disperse the plants across an area over time.
Walking onions taste and cook similarly to the common onion, with a range from sweeter to sharper depending on exact variety obtained. The ones I've grown have been sharper, more toward the red-onion end of the spectrum — or maybe between yellow and red. It's fun to watch them slowly spread themselves. They do not replant themselves quickly or successfully enough to actually create a real spreading problem for the gardener.
Occasionally the reproduction-in-place even gets somewhat comical. The rate of germination can sometimes be low enough that only one or two child onions grow at the top. If this occurs and the parent stalk is a strong one, the children can grow all the way to maturity at the top of the stalk, without ever falling over. Apparently they are able to get nutrients from the parent even when deprived of the chance to root in the ground. When this happens, yet another set of bulbs can germinate at the top of what is now a three-generation onion stack!
Grow your own
With a plant as hardy and eager to root as this variety, it's quite easy to grow your own. Simply obtain seeds or bulbs from a supplier (also known as Tree Onions if you're searching around) and bury them very shallowly in moderate soil that gets some sun. Water lightly but regularly, always allowing the soil to dry a bit below just the surface between waterings. If the flowering stalk appears, you're doing OK. Any mold or mildew indicates overwatering, and wilting indicates too much sun or temperatures too high (though in general onions are pretty good with sunny locations) or underwatering.
Enjoy your new toddlers! ...Both at play and in tasty dishes.