These ingredients for Food have been added with the R24 update.
These eggs will not be "dropped" by Blizzard Chizzards nor any kind of Chizzards when you kill or dismiss them. Blizzard Chizzards look like a bright blue and white colored hybrid of a chicken-like animal and a reptile-like one (lizard).
To receive Blizzard Chizzard Eggs you will have to "pull" Pet Blizzard Chizzards with your arctek gauntlet (no Power Cell is needed) like you would pull any block for mining or harvesting a short while after you fed your Pet Blizzard Chizzard.
Usually Blizzard Chizzards will only give you their eggs if you have fed them their favorite Food that is displayed in their respective Pet Window when right-clicking the Pet or interacting with it (default key "F").
Usually 1-3 eggs can be harvested each time. You can only harvest more eggs from the same Pet Blizzard Chizzard after washing it with a Washer and then feeding it once more when it gets hungry again.
Corrupted Chizzards do not "lay" any eggs as yet.
Currently (as of R27 in January 2016), players cannot breed creatures, and no creatures will hatch from eggs.