Slice each chicken breast in half horizontally to create 4 thin cutlets. Pat completely dry on both sides. Mix salt, pepper, and smoked paprika together and rub evenly over both sides of each cutlet.

Heat a 12-inch saute pan over medium-high heat for at least 3 minutes. Add oil and swirl to coat. Add chicken without moving it. Lower to medium and cook 3 to 4 minutes. If it sticks when you try to flip, it needs more time.

Flip each piece, add 1 tablespoon butter, and swirl. Cook the second side about 2 minutes until deep golden brown and internal temperature reads 160 degrees F. Remove to a plate, cover loosely, and rest. Leave pan juices in the pan.

Bring a pot of salted water to a boil. Cook fettuccine about 10 minutes until al dente. Reserve 1 cup pasta water before draining. Drain and drizzle with a little olive oil. Set aside.

In the same pan, add 3/4 cup butter over medium heat. Once melted and bubbling, add garlic and cook 1 minute until fragrant. Do not brown the butter.

Slowly pour in heavy cream while stirring. Add salt, pepper, cayenne, and nutmeg. Cook over medium heat for 2 to 3 minutes until gentle bubbles form at the edges only. Do not boil or the sauce will break. Reduce to medium-low.

Add Parmesan a few tablespoons at a time, stirring constantly between additions until fully melted. Taste and adjust seasoning.

Add fettuccine to the sauce in thirds, tossing to coat between each addition. Slice rested chicken against the grain into strips.

Plate pasta and arrange sliced chicken on top. If sauce is too thick, add reserved pasta water a tablespoon at a time. Garnish with extra Parmesan and fresh parsley. Serve immediately.