Bring a large pot of salted water to a boil and cook the spaghetti according to package directions. Aim for an al dente texture so the pasta holds up well in the creamy sauce. Drain and set aside.
Pat the chicken strips dry with paper towels. Season them with Cajun seasoning, smoked paprika, salt, black pepper, and Parmesan cheese. Press the Parmesan onto the chicken so it forms a light coating.
Heat olive oil and half of the butter in a large skillet over medium-high heat. Add the chicken and cook until golden brown and fully cooked. The Parmesan coating should develop a delicious crust.
During the final minute of cooking, add a portion of the minced garlic to the skillet. Stir gently so the garlic becomes fragrant without burning. Remove the chicken and set it aside.
In the same skillet, melt the remaining butter and sauté the rest of the garlic. Pour in the chicken broth and heavy cream, stirring constantly. Allow the mixture to come to a gentle simmer.
Add the cream cheese and whisk until completely smooth. Gradually stir in the mozzarella, cheddar, and Parmesan cheese. Continue stirring until the sauce becomes creamy and velvety.
Sprinkle in the Italian seasoning, dried basil, and optional red pepper flakes. Taste the sauce and adjust seasoning if needed. Let it simmer briefly until slightly thickened.
Add the cooked spaghetti directly to the skillet. Use tongs to toss the pasta thoroughly so every strand is coated in the creamy Cajun sauce. Allow it to warm through for another minute.
Return the cooked chicken to the skillet or arrange it over the pasta when serving. This helps preserve the crispy Parmesan coating while adding a beautiful presentation.
Sprinkle freshly chopped parsley over the finished dish. Serve immediately while the sauce is hot, creamy, and perfectly smooth.