Bring a large pot of generously salted water to a rolling boil. Add the fettuccine and cook according to package directions until al dente, typically 8-10 minutes. Reserve 1/2 cup of pasta cooking water before draining. Drain the pasta in a colander and set aside.
While the pasta cooks, melt the butter in a large Dutch oven or deep skillet over medium heat. Once the butter is fully melted and beginning to foam, add the chopped onion, red bell pepper, and celery. Sauté the vegetables, stirring occasionally, until they become soft and the onion turns translucent, about 6-8 minutes.
Add the minced garlic to the softened vegetables and stir constantly for about 2 minutes until fragrant, being careful not to let it brown or burn.
Add the thawed crawfish tails along with any liquid from the package, Cajun seasoning, black pepper, and cayenne pepper to the pot. Stir well to combine and cook for 3-4 minutes, allowing the crawfish to absorb the seasonings.
Sprinkle the flour evenly over the crawfish and vegetable mixture. Stir continuously and cook for 1-2 minutes to eliminate the raw flour taste and create a roux base for the sauce.
Gradually pour in the half-and-half while stirring constantly to prevent lumps from forming. Continue stirring and cook until the mixture begins to gently simmer and thicken slightly, about 3-4 minutes.
Reduce the heat to medium-low and add the Velveeta cubes, sour cream, and freshly grated Parmesan cheese. Stir constantly until all the cheese has completely melted and the sauce is smooth and creamy, about 3-5 minutes. If the sauce seems too thick, add a splash of the reserved pasta water to reach desired consistency.
Add the cooked and drained fettuccine to the creamy crawfish sauce. Using tongs or a large fork, toss the pasta gently but thoroughly to ensure every strand is coated with the rich sauce. Stir in the sliced green onions and chopped fresh parsley.
Taste and adjust seasoning if needed, adding more Cajun seasoning or cayenne pepper for extra heat. Serve immediately while hot, garnished with additional Parmesan cheese and green onions if desired.