Boil a large pot of salted water and cook the pasta according to package instructions until al dente. Reserve some pasta water before draining.
In a skillet, heat olive oil over medium-high heat. Add chicken and sprinkle with Cajun seasoning. Cook until fully cooked and no longer pink, about 6-8 minutes.
Lower the heat and add heavy cream or half-and-half. Whisk in Parmesan cheese until melted and the sauce is creamy. Let it simmer to thicken slightly.
Add the cooked pasta to the skillet and toss to combine. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Serve immediately, garnished with extra Parmesan and parsley if desired.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3 days.