Cut the carrots and zucchini into long, fine strands or ribbons by drawing a vegetable peeler down the length of them.
Pour 1/2 inch of boiling water into a saucepan and add the carrots. Cover the pan, and half-boil, half-steam the carrots over moderate heat for 2-3 minutes. Add the zucchini and cook for 1-2 minutes longer (zucchini cook quickly; don't let them become waterlogged). Drain.
Transfer the vegetables to a bowl, add the pesto and a little seasoning, mix well, and serve at once.