Freshly bought carrots turn black (like coal) on peeled surfaces in minutes if not seconds. I wonder why and why are these special.  Obviously it is not black rot. The carrots taste normal, albeit not too sweet. Too much fertilizer nitrates? Or just contain lots of starch like in potatoes? The carrots were clean to begin with and I washed my hands too :-)   Update: I live in Denmark and these carrots are from Spain, perhaps Canary Islands, fresh veges seem like a bit of a struggle here, hence I am surprised. 
This looks to me like simple oxidation. It is just that your batch shows it more than others.   It is completely normal for plants of the same species to have very different amounts of the same chemical compound. Think of capsaicin in peppers, which vary from sweet to your-intestines-will-be-on-fire-for-days, anthocyanins in tulips (or carrots) which can have none (whitish) to be chock full of them (dark purple), or the aroma compounds which are concentrated in oil roses and absent in the roses bred for the grocery store shelves.   Oxidation browning occurs when oxygen from the air activates an enzyme in the fruit (or vegetable) which then reacts with phenolic compounds in the plant tissue. You must have happened upon a batch of carrots which has high amounts of phenolics, or an unusually efficient enzyme, or large amounts of the enzyme.  