Halve both chicken breasts horizontally into 4 even cutlets, about 1/2 inch thick. Pat dry and season with the chicken salt, garlic powder, pepper, and paprika.

Heat chicken oil over medium-high heat, add cutlets, and reduce to medium. Cook 3–4 minutes on the first side; flip, add chicken butter, and cook 2–4 minutes more until 165°F, dividing oil and butter equally if using 2 batches.

Rest chicken 5 minutes. Meanwhile, boil fettuccine in water with the pasta salt according to package directions until al dente; reserve 1 cup cooking water and drain.

Melt the sauce butter over medium-low heat and cook garlic 30–60 seconds until fragrant. Add cream, sauce pepper, cayenne, and sauce salt to taste; heat 2–3 minutes until gently bubbling at the edges.

Remove from heat and stir in 1 cup Parmesan gradually until melted. Toss with drained fettuccine, adding reserved pasta water 2 tablespoons at a time if needed.

Divide pasta among 4 bowls. Slice the rested chicken and add 1 cutlet per bowl; top with parsley and the remaining 1/2 cup Parmesan.