Bring a large pot of salted water to a boil. Cook the linguine according to package directions. Reserve 1/4 cup of pasta water, then drain and set the pasta aside.

Season the chicken breasts on both sides with Cajun seasoning, Italian seasoning, salt, and black pepper.

Heat olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook for 4-5 minutes per side until golden-brown and cooked through. Remove the chicken and set it aside.

In the same skillet, reduce the heat to medium and add butter. Once melted, sauté the minced garlic for 30 seconds until fragrant.

Pour in the heavy cream and chicken broth. Bring the mixture to a gentle simmer.

Stir in the Parmesan cheese (and mozzarella, if using) until completely melted and the sauce is smooth.

Add the cooked linguine to the skillet, tossing to coat the pasta in the sauce. If it seems too thick, add a splash of reserved pasta water.

Return the Cajun chicken to the skillet, nestling it among the linguine. Simmer for another 1-2 minutes to combine the flavors.

Garnish with chopped parsley or green onions and serve warm.