Fill a large pot with water, add a generous pinch of salt, and bring to a boil. Cook the linguine according to package directions until al dente. Reserve 2 tablespoons of the pasta water, then drain and set the pasta aside.

While the pasta cooks, pat the chicken dry and rub both sides with the Cajun seasoning.

Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the chicken and cook without moving for 6–7 minutes, until a golden crust forms.

Flip the chicken and cook another 6–7 minutes, until the internal temperature reaches 165°F (74°C). Transfer the chicken to a plate and let it rest for 5 minutes.

Lower the heat to medium-low in the same skillet. Add the minced garlic and sauté for about 1 minute until fragrant, taking care not to brown it.

Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan until the sauce becomes smooth. Taste and season with salt and black pepper. If the sauce is too thick, stir in a splash of the reserved pasta water to loosen it.

Add the cooked linguine to the skillet and toss so every strand is coated with sauce.

Slice the rested chicken and arrange it on top of the linguine. Garnish with chopped parsley and serve immediately.