I've never seen a kid who didn't like this veggies-and-pasta dish. The secret to its flavor? It's cooked over low heat for several minutes so the creamy sauce is absorbed into the noodles. For a version that's not quite as rich, use light cream to replace up to half of the heavy cream. Vegetarians can replace the chicken broth with vegetable broth.
In a large pot, bring 4 to 5 quarts of water to a boil and add 1 tablespoon of olive oil and 2 teaspoons of salt to the water.
Meanwhile, in an enameled Dutch oven or another large nonreactive casserole, melt the butter over low heat. Stir in the garlic and warm gently for 1 minute. Add the broth, vegetables, and 1/4 teaspoon of salt. Bring the mixture to a simmer.
Cover the pan and continue to simmer the vegetables undisturbed for 3 minutes. Then stir in the cream. Remove the pan from the heat and leave it covered. Add more salt to taste, if needed.
Once the water has reached a boil, gradually add the fettucine to it. Cook the pasta according to the package directions, then drain.
Quickly bring the vegetables back to a simmer and add the drained pasta. Continue to simmer the mixture over medium-low heat for 3 to 4 minutes while carefully tossing the noodles up from the bottom of the pan with tongs or two forks.
Remove the pan from the heat and sprinkle in half of the Parmesan cheese. Toss once more. Serve at once, using the parsley and remaining cheese for garnish. Makes 4 to 5 servings.