Pat the chicken breasts dry with paper towel and rub Cajun seasoning all over. Let sit for 10 minutes.

Heat skillet over medium-high heat and add olive oil. Sear chicken for 5-6 minutes on each side until golden brown and cooked through.

In a pot, bring salted water to a boil. Cook linguine according to package instructions until al dente, about 9-11 minutes. Reserve ½ cup of pasta water, then drain.

Return skillet used for chicken to stovetop, reduce heat to medium, and melt butter. Add minced garlic and sauté for about 1 minute until fragrant.

Pour in heavy cream and let simmer for 3-4 minutes, stirring occasionally until slightly thickened.

Whisk in grated Parmesan cheese until melted and smooth. Adjust thickness with reserved pasta water if necessary.

Add cooked linguine to the sauce and toss to coat evenly. Heat through for 1-2 minutes.

Slice chicken and serve on top of linguine. Garnish with parsley and red pepper flakes, if desired.