A while ago I read a book about the Russian Civil War (it was Blood on the Snow by Emanuel Litvinoff) in which the characters frequently drank coffee made out of acorns and tea made out of carrots. I tried naively making carrot tea by grating some carrots and pouring hot water on them, like I would make ginger tea. But the resulting brew did not taste strongly of carrots.  How is carrot tea brewed--what part of the carrot is used? I would also be interested to know whether there are any other countries in which this has ever been a popular drink. 
Wash, dry, shred, cut finely or julienne the carrots. Dry it on a sheet of parchment paper until almost all of the moisture is evaporated. Bake it in an oven on low heat until brown.  Left: result, Right: brewed. Source 