Cook fettuccine according to package directions.
In the meantime, melt butter in a large sauté pan over medium heat. Add garlic and cook until garlic is fragrant, about 30 seconds.
Add cream, 1/3 cup at a time. Alternate with flour, whisking in flour one tablespoon at a time. Whisk until flour is incorporated and the mixture is smooth.
Add Cajun seasoning, nutmeg, and white pepper.
Remove pan from heat. Stir in Parmesan cheese, mixing until combined. Season with salt.
Add crawfish tails and fettuccine. Thin sauce with additional cream if it gets too thick.
Garnish with fresh parsley if desired.