You're leaving out the bit where you find a knife and a cutting board, and then you wash the knife and the cutting board, and the bit where you throw away all the peel you cut off, and the bit where some of the peel winds up on the floor so you have to bend over and pick it up, and... wait, can't you just buy packaged prepeeled babby carrots anyway? They sell 'em at my local supermarket.
I can't tell if this is tongue-in-cheek or not, but I'll reply seriously anyway:
When I want a carrot I grab one out of the fridge, grab the peeler off of the counter, pull my compost box out from under the sink and peel it directly into the compost. Why would you need a cutting board?!