This article titled "How To Grow Sprouted Onions" at Alternative Gardening talks about exactly that. I had no idea. All this time, if I didn't eat an onion in time, I would simply plant the whole thing as-is in the soil.
Growing vegetables from food waste is a great lesson for kids and also makes great science experiments Teach students how to regrow food and pick a food to regrow as a class. Could use a food from a students leftover lunch.