Bring 4 quarts of heavily salted water to a rolling boil and cook fettuccine until al dente; reserve 1/2 cup pasta water and drain.
Dredge chicken cutlets in blackened seasoning, pressing firmly to adhere the spices to the surface.
Heat olive oil in a large cast-iron skillet over medium-high heat until shimmering.
Sear chicken for 5-6 minutes per side until a dark crust forms and internal temperature reaches 165°F (74°C). Remove and tent with foil.
In the same skillet over medium heat, melt butter and sauté minced garlic for 60 seconds until fragrant.
Deglaze the skillet with heavy cream, scraping the fond from the bottom of the pan; bring to a light simmer.
Reduce heat to low and whisk in parmesan cheese gradually until the sauce is emulsified and thickened.
Adjust sauce consistency with reserved pasta water if necessary and season with salt and pepper.
Slice the rested blackened chicken into 1/2-inch strips.
Toss the cooked fettuccine into the cream sauce until thoroughly coated.
Divide pasta into bowls, top with sliced chicken, and garnish with chopped parsley.