Melt the butter: In a large skillet over medium heat, melt the butter until it foams slightly. Add the minced garlic and cook for about 1 minute, stirring constantly so it doesn't brown.
Brown the sausage: Add the sliced sausage to the skillet and cook until golden on the edges, about 5 minutes. Remove the sausage and set it aside on a plate.
Add the cream and broth: Pour the heavy cream and chicken broth into the skillet, stirring to combine with the browned bits. Bring the mixture to a gentle simmer over medium-low heat.
Season the sauce: Stir in the Cajun seasoning, cayenne pepper, salt and black pepper. Simmer for 2 minutes, stirring often, so the flavors blend into the cream.
Melt in the parmesan: Reduce the heat to low and whisk in the parmesan cheese a little at a time. Keep whisking until the sauce is smooth and coats the back of a spoon, about 3 to 4 minutes.
Return the sausage: Add the browned sausage back into the skillet and simmer for 2 more minutes so it warms through and picks up the sauce flavor.
Cook the pasta: While the sauce simmers, cook the fettuccine in salted boiling water according to package directions until al dente. Drain, reserving 1/4 cup of the pasta water.
Toss and finish: Add the drained pasta directly to the skillet and toss until every strand is coated, adding a splash of reserved pasta water if the sauce needs loosening. Garnish with chopped parsley and serve warm.