When your fresh garlic gets a little old, sometimes a little green shoot will appear in the clove. Here's something you can do so they don't go to waste.
Peel each clove without damaging it. Place in root side down in a clear glass container. Be careful to discard any cloves that look like they have started to rot - they will continue to do so in the container. Add just enough water to cover the root end (no more a few millimetres). Place in a bright window. Replenish the water daily. Soon you will see new root growth and green shoot growth.
The shoots are completely edible. The shoots that I grew are quite pungent and sharp. They are fantastic as a garnish garlic dishes that I want to be even more garlicky or as a milder flavour in salads or any fresh mixture of veggies.