Preheat a grill or grill pan to medium heat.
Rub chicken breasts all over with 1 tablespoon olive oil.
Season with Italian seasoning, garlic powder, paprika, salt and pepper.
Place chicken on grill and cook for 6 - 8 minutes per side, or until the internal temperature reaches 165°F (74°C).
Remove from grill and allow to rest for 5 minutes.
Slice into thin strips. Set aside and keep warm.
Prepare pasta according to package directions. Drain. Set aside.
Place butter and 2 tablespoons olive oil into a medium skillet. Place over medium heat.
When butter has melted and is hot (do not burn), add garlic. Sauté for 1 - 2 minutes until fragrant.
Stir in heavy cream. Bring to a gentle simmer.
Gradually whisk in Parmesan cheese, stirring until the sauce is smooth and creamy.
Add 1/2 teaspoon salt, 1/4 teaspoon pepper and nutmeg, to taste.
Stir in mozzarella cheese and melt.
Toss the cooked pasta with the Alfredo sauce until well coated.
Add the sliced chicken on top and gently mix to combine.
Plate pasta in a serving bowl or plate or dish onto individual bowls or plates.
Sprinkle with parsley.
Serve with extra Parmesan cheese on the side.