Use a large pot to boil the fettuccini according to the package instructions while you prepare the alfredo sauce. Be sure to salt your water.
Drizzle the chicken with olive oil, rubbing on both sides. Season with salt and pepper, and cajun seasoning if using.
In a large pan over medium-low heat, add in 2 tablespoons of olive oil. Place the chicken breasts in the pan and cook about 5 minutes, flip, reduce heat to low, and continue cooking about 5 more minutes or until cooked through. Set aside.
In the same pan over medium-low heat, melt the butter. Add in the minced garlic and stir until fragrant, about 1 minute, scraping up the brown bits in the pan.
Pour in the half-and-half, heavy cream, 1/2 tsp salt, and 1 tsp pepper. Stir to incorporate, and slowly bring it to a simmer until it starts to thicken, about 5 minutes. Add the Parmesan cheese and whisk until smooth, allowing the cheese to melt. Taste and adjust salt if needed.
Toss the pasta in the sauce until it’s well coated. Don't worry if the sauce seems a little thin; the starch from the pasta will quickly thicken it. Top with the sliced chicken, sprinkle with parsley (optional), and serve immediately.