I use a veggie peeler to make the carrot ribbons and a mandolin to make the zucchini ribbons. The veggie peeler didn't work well for me for the zucchini (could be the type of peeler I have), but you can try it if you don't have a mandolin. If using a mandolin, you want to use a very thin setting. When making the carrot strips, rotate the carrot a quarter turn every 1 or 2 strips so that you end up making a square around the core of the carrot. Stop when all that's left is the core.
And, of course, a little Parmesan cheese sprinkled on top makes all the difference.
Note: I've found yellow (like crook-neck) squash has too many seeds and too much moisture to work well when cut in thin strips. This summer I'll use yellow zucchini for a beautiful 3-color dish.
Carrot and Zucchini Ribbons
2 teaspoons olive oil
4 large carrots, scraped and made into strips
4 small zucchini, sliced very thin
kosher salt and fresh black pepper to taste
Parmesan cheese for serving
Heat a large (12-inch) non-stick skillet over medium-high heat until hot. Add the oil and heat for 10 seconds. Add the carrots and zucchini, and cook, stirring and tossing often with tongs, until the vegetables are al dente, 3-5 minutes. Season with salt and pepper, sprinkle with Parmesan, and serve.
Makes 4-6 servings.