I had some carrots in storage that had started growing so I potted them up in January (I had the itch- baddddd). They are doing great and now a couple have flower buds on them!!! Once they begin flowering they'll go outside during the day so the pollinators can get to them. I think I'll have seeds in a few months- which will give me plenty of time to grow carrots from their seed this year.
So, although carrots are biannuals, you can get seed and grow them yearly.
Oh, and they make really pretty houseplants in a southfacing window. Easily as pretty as ferns, if not prettier.