Slice each chicken breast in half horizontally to create 4 thin cutlets. Mix together salt, pepper, and smoked paprika. Pat chicken dry with paper towels, then season both sides.

Heat large saute pan over medium-high for 3 minutes. Add oil and swirl to coat. Place chicken in hot pan without overcrowding. Cook 3-4 minutes on first side without moving.

Flip chicken once it releases easily, add 1 tablespoon butter, and cook another 2 minutes until golden brown and internal temperature reaches 165°F. Transfer chicken to a plate, cover to keep warm, and leave juices in pan.

Bring large pot of salted water to a boil. Add fettuccine and cook until al dente, about 10 minutes. Reserve 1 cup of pasta water, then drain noodles. Drizzle lightly with olive oil and toss to prevent sticking.

In the same pan used for chicken, melt 3/4 cup butter over medium heat. Add garlic and saute 1 minute until fragrant.

Slowly pour in heavy cream while stirring. Add salt, pepper, cayenne, and nutmeg. Simmer gently (no boiling) for 2-3 minutes until small bubbles form.

Gradually stir in Parmesan, a few tablespoons at a time, until melted and smooth. Taste and adjust seasoning.

Add fettuccine to sauce in batches, stirring to coat evenly. Slice chicken thinly across the grain. Either layer it on top of pasta or stir it in.

If sauce thickens too much, loosen with a few tablespoons of reserved pasta water. Garnish with extra Parmesan and chopped parsley. Serve immediately.