Cook the pasta. Bring a large pot of salted water to a boil. Add the pasta and cook until al dente according to the package directions. Before draining, reserve about 1/4 cup of pasta water. Drain and set aside.
Season the chicken. Heat the olive oil in a large skillet over medium heat. Add the diced chicken in a single layer and season with Italian seasoning, minced garlic, salt, and black pepper.
Cook the chicken. Cook for approximately 6–8 minutes, stirring occasionally, until lightly golden and completely cooked. Chicken should reach an internal temperature of 165°F (74°C). Transfer it to a clean plate.
Make the roux. Reduce the heat to medium if necessary and melt the butter in the same skillet. Sprinkle in the flour and cook for about 1 minute, stirring constantly.
Build the cream sauce. Slowly whisk in the chicken broth until smooth. Gradually add the half-and-half while continuing to whisk.
Bring the mixture to a gentle simmer and cook for 3–4 minutes, whisking frequently, until slightly thickened.
Add the pesto. Remove the skillet from the heat and stir in the basil pesto until evenly incorporated.
Add the cheese. Gradually stir in the Parmesan and mozzarella, adding a little at a time and mixing until the cheese is completely melted and the sauce is creamy.
If the sauce becomes thicker than desired, stir in a splash of reserved pasta water until it reaches your preferred consistency.
Combine. Return the cooked chicken and pasta to the skillet. Toss gently until everything is evenly coated in the Creamy Chicken Pesto Pasta sauce.
Taste and adjust the salt and pepper as needed. Serve warm with chopped fresh basil and extra Parmesan.