Cook the spaghetti according to package directions until al dente. Drain and set aside.

In a large skillet, heat olive oil and butter over medium-high heat. Add chicken pieces and cook until golden brown and cooked through. Remove and set aside.

Add the diced onion to the same skillet and cook until softened. Stir in minced garlic and cook for 30 seconds.

Sprinkle flour over the mixture and stir to coat evenly.

Pour in the broth and heavy cream, stirring and simmering until the sauce begins to thicken.

Add cubed cream cheese and shredded cheeses, stirring until melted and the sauce is smooth and creamy.

Return the cooked chicken to the skillet, stirring to coat in the sauce.

Add the cooked spaghetti to the skillet and toss until each piece is coated in the creamy sauce.

Simmer 1–2 minutes to let the flavors meld.

Serve hot, garnished with chopped parsley if desired.