The onions are chopped and then put through a grinder extracting the onion juice, the liquid of which is used in making the bagel instead of water and the remaining onion shreds are dehydrated, and the bagel gets coated with their pungency. The onion extraction gives these bagels intense onion flavor.
That’s the art of the onion bagel as explained to me by Kevin Gravito, the bagel baker at Rose Foods. He also said they’re more labor intensive to make than other bagels.