The family members who taught me to cook have always tossed carrot tops/greens into the compost pile or the trash (and my regular grocery store carries carrots without tops), so I've never really thought about cooking with them before. Today, however, I bought some carrots with fresh, green tops, and it seems a shame to waste them. Can I safely cook with them, and if so, how?
I've never had them, but they are indeed edible. Due to the high amount of potassium in them they can be bitter. The World Carrot Museum (lol) even has an entire page for carrot greens, including several recipes.
They ARE edible and are highly nutritive, rich in protein, minerals and vitamins. The tops of the carrots are loaded with potassium which can make them bitter, so the use of them in food is limited, but there some ideas and recipes below. The tops are antiseptic and can be juiced and used as a mouthwash.
However, it is edible, so you may mix some in with a mixed lettuce salad. You may also use it for garnish. Combine your common sense and your creative skills, and invent something! That's what makes cooking fun. It is a form of art. Carrot greens are high in vitamin K, which is lacking in the carrot itself.
Carrot tops are an outstanding source of chlorophyll, the green pigment that studies have shown to combat the growth of tumours. Chlorophyll contains cleansing properties that purify the blood, lymph nodes, and adrenal glands. Scientists have been unable to synthesize chlorophyll in the laboratory, but green plant foods contain sufficient quantities to protect the human body.
I like hobodave's answer, but I'll put my .02 bucks on a negative answer: I tend to throw cooking debris in the stock pot. Onion skins, garlic peels, anything I might otherwise throw away. It's stock, right? Stock and stuffing exist to make use of leftovers.
But don't do this with carrot tops, it'll make your stock taste wonky. Had to make thanksgiving gravy with store broth that year. Blech.
Carrot greens are a great substitute for flat-leaf parsley in many dishes, especially ones that will be cooked, as the carrot greens tend to handle heat better than parsley. I use them in Beet Burgers along with the carrots themselves, with terrific results. You can also throw them in to seasoned breadcrumbs for a great topping for casseroles, etc.
They are definitely edible, with a more herbal carrot taste. Cooking with "produce offal" has become fairly popular, which means you can find a number of recipes designed to use carrot tops and other "garbage" parts of your produce if you don't feel up to experimentation, but would like to explore the idea of generating less food waste.
The ferny leaves on the top are nicely delicate and can be used anywhere you might use other leafy greens, for a slightly different taste. I have personally used them to create a non-basil pesto, and they can make a lovely edible garnish with your meal or an addition to mixed raw greens.
The tops as a full unit tend to be better when cooked; I've found them particularly good when sauteed quickly so the stems soften and the leaves get a bit crisp. If you prefer a more uniform texture (I like the variation), you can remove the leaves to toss in at the end so they only soften; they'll cook much faster than the stems. Any combination of seasonings you might use for sauteed or roasted carrots would serve well here, too, as the flavor is very similar.