Fill a large pot 2/3 full with hot water. Set it on the stove over high heat and add a couple teaspoons of salt to the water. Cover the pot.
While your water is boiling, rinse and peel your carrots. Trim off and discard the ends. Cut each carrot in half so that it is 3-to-4 inches long. Cut each piece in half the long way to make the carrots thinner. If you have a thick carrot, you might want to cut it in half again the long way.
When the water is boiling, add the carrots to the pot. When the water returns to a boil, lower the heat and cover the pot. Boil the carrots for 10 minutes, or until they are done to your liking. (Check by inserting a fork in one or tasting it.)
While the carrots are cooking, stack your basil leaves and roll them tightly into a cylinder shape. Slice your cylinder of basil into pieces about 1/4 inch wide. This will give you ribbons of basil (chiffonade).
When the carrots are done, drain them in a colander in the sink and run some cold water over them to stop the cooking. Transfer the carrots to your serving bowl and add the rest of the ingredients. Gently toss everything together with two spoons. Serve at room temperature. (You can make it one or two hours ahead of time and let it marinate at room temperature, if you wish.) Store leftovers in the refrigerator for up to five days.