Peel all of the carrots. Cut 1 carrot into thin disks. Chop up 2 carrots into bits. Save the largest carrots and, using a vegetable peeler, cut long flat strips of carrot by sliding the peeler lengthwise down the carrot. When you have gotten as many strips as possible, chop the rest of the carrots.
Heat the oil and/or butter in a wide 4-quart/4-l pot over medium-low heat. Add the onion