Slice each chicken breast in half horizontally to create 4 thin cutlets. Pat dry with paper towels. Mix salt, pepper, and smoked paprika and rub evenly over both sides of the chicken.

Heat a 12-inch saute pan over medium-high heat for 2 minutes. Add oil and swirl to coat. Place chicken in pan and do not move it. Lower to medium heat and cook 3 to 4 minutes. Flip, add butter, and cook another 2 minutes until golden brown and the internal temperature reaches 165 degrees F. Remove to a plate, tent with foil, and leave all juices in the pan.

Bring a large pot of salted water to a rolling boil. Cook fettuccine 9 to 10 minutes until just al dente. Reserve 1 cup of pasta water before draining. Toss drained pasta with a light drizzle of olive oil to prevent sticking and set aside.

In the same pan over medium heat, melt the butter for the sauce. Add minced garlic and saute 3 to 4 minutes until fragrant and lightly golden. Slowly pour in the heavy cream, stirring as you go. Add salt, pepper, cayenne, and nutmeg. Cook 2 to 3 minutes until small bubbles appear at the edges. Do not boil. Reduce heat to medium-low.

Add the shredded Parmesan a few tablespoons at a time, stirring after each addition until fully melted and the sauce is smooth and silky. Taste and adjust seasoning if needed.

Add the cooked pasta in batches, tossing to coat evenly. If the sauce tightens, loosen with reserved pasta water a tablespoon at a time. Slice the rested chicken across the grain into strips and arrange on top. Garnish with extra Parmesan and fresh parsley. Serve immediately.