Carrots
I saw something on youtube about leaving them in an bowl of water, but mine just started to rot. I have not tried with wet paper.
So I have replanted the tops of carrots. From 4 replants straight in the earth, 2 rotted away and 2 grew roots during 2 very wet weeks. Unfortunately, because I pulled them from the earth to check, I might have demaged them. I will just have to be patient and wait for the green leaves to show.
What got me interested in this was a story of someone who claimed to be
eating the same carrots for 9 years (!) in a permaculture book. I forgot which book and can not find it anymore, sorry.
Unions
jeremiah bailey wrote:I learned about doing this with onions when I was a boy. Has anyone tried taking the stub that you'd replant and cut it radially into pieces like a pizza? I have sneaking suspicion that it'd propagate this way. Make sure you have some rootlets on each piece.
Actually, after looking around, I found this: http://www.instructables.com/id/Grow-Onions-from-Discarded-Onion-Bottoms/ Which describes sprouting the bottom and then cutting the separate stalks away from the root section. I think I'm going to try both ways with the next batch of onions we cook with.
That made my day

Thank you very much.
Would be interesting to see if it will regrow if you just cut the union off and leaving the root in. Will be tricky to do without disturbing the roots. I guess it will as there are many union species that can be used by cutting of the top leaves to be used as unions.
@jeremiah bailey
Any follow up on the experiment of cutting the bottom of the union to replant?