I clip off any tops that have bulbils, just replanting the whole head right away in a marked spot. Early the next summer, when I am harvesting my regular crop, I'll dig those as some of the start for the following year.

If they are true potato onions there should be seeds there not bulbils. They can be planted back, but tend to have very poor germination. The resulting plants can be extremely variable since the actual bulbs are essentially hybrids. Some of the seedlings may be worth saving.

Kelly Winterton in Utah has done just that and the improved Green Mountain multiplier is one of his results, after some years of reseeding and culling.