Bring a large pot of salted water to a boil. Add spaghetti and cook until al dente, about 8-10 minutes. Reserve half a cup of pasta water, drain and set spaghetti aside.

Heat the olive oil in a large skillet over medium heat. Season chicken with salt and pepper, then add to skillet. Cook chicken for 6-7 minutes per side until golden brown and cooked through. Remove and slice into strips.

In the same skillet, sauté minced garlic for about 1 minute until fragrant. Pour in heavy cream and scrape any bits left from the chicken. Let the sauce simmer for 1 minute to thicken.

Stir in freshly grated Parmesan cheese until melted and smooth. Adjust thickness with reserved pasta water if necessary.

Combine the cooked spaghetti and sliced chicken into the skillet, tossing to coat with the sauce. Heat through for about 2-3 minutes.

Serve immediately, garnished with extra grated Parmesan cheese and chopped parsley if desired.