Bring a large pot of salted water to a boil and cook the spaghetti until al dente. Drain and set aside.
In a large skillet, heat olive oil and 2 tablespoons of butter over medium-high heat. Add the chicken pieces, season with salt, pepper, garlic powder, paprika, and Italian seasoning, then sauté for 6–8 minutes until golden brown and cooked through. Remove the chicken and set aside.
In the same skillet, melt the remaining tablespoon of butter. Add the minced garlic and cook for 30 seconds until fragrant.
Pour in chicken broth and heavy cream, stirring to combine. Add the softened cream cheese and stir until completely melted and smooth.
Gradually add the Parmesan and mozzarella cheese, whisking until the sauce thickens into a rich, velvety consistency. Adjust seasoning with salt and pepper as needed.
Add the cooked spaghetti to the sauce and toss gently to coat every strand in the creamy cheese mixture. Simmer for 2–3 minutes to let the sauce fully absorb into the pasta.
Return the chicken to the skillet, mixing gently so the flavors combine. Sprinkle with crushed red pepper flakes if desired for a touch of heat.
Garnish with chopped parsley and serve warm with extra Parmesan on top.