Pat the chicken breasts dry and pound to an even ½-inch thickness. Season both sides generously with Cajun seasoning.

Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken and cook for 5-7 minutes per side, until golden brown, blackened, and cooked through. Remove from the skillet, let rest for 5 minutes, then slice into strips.

While the chicken cooks, bring a large pot of heavily salted water to a boil. Cook fettuccine according to package directions until al dente. Reserve 1 cup of the pasta water before draining.

In the same skillet, melt the remaining 5 tablespoons of butter over medium heat. Add the minced garlic and cook until fragrant, about 30 seconds.

Pour in the heavy cream and bring to a gentle simmer, scraping up any flavorful bits from the bottom of the pan. Reduce the heat to low.

Gradually whisk in the freshly grated Parmesan cheese until the sauce is smooth. Season with a pinch more Cajun seasoning, salt, and pepper to taste. If the sauce is too thick, stir in a splash of reserved pasta water.

Add the drained fettuccine and sliced chicken back to the skillet. Toss to combine everything until the pasta is well coated. Serve immediately, garnished with fresh parsley.