I met red carrots in Israel. I actually had one hidden stand inside the market of jerusalem old city. He use to sell wild red carrots among othe strange wlld plants noone ever heard of.
Since I got here i found a similar plant in gourmet supermarket. A bit smaller and with thinner skin. But I havn't tried this yet.
The kind I used in israel are appearntly older than the yellow kind, and only recently begun to be grown commerceily. They're not exactly red but sort of beet-purple with a yellow/orange center - beautiful. Like beet it's color stains. They have much thicker skins. The arabs use to stuff them because of they're cone link shape. The flavor - a bit sweeter than regular carrots with a few different subtastes.
I tried several things with them - stuffed with rice, pied slicd arranged in circular patterns on top, jammed, icecreamed, sliced and candied, souped, gnocchied, etc.