Preheat the oven to 375°F (190°C).
Bring a large pot of water to a boil and cook the penne according to package directions, omitting salt; add the spinach to the boiling water during the last minute of cooking.
While the pasta cooks, heat a large nonstick skillet over medium-high and lightly spray with cooking spray.
Add the chicken and dried basil to the skillet and cook, stirring, about 3 minutes until the chicken is cooked through.
Stir in the jarred spaghetti sauce, minced garlic, and drained diced tomatoes; bring to a boil, then reduce heat and simmer 3 minutes.
Stir the cubed Neufchâtel cheese into the chicken mixture until incorporated and warmed through.
Drain the pasta and spinach in a colander and return them to the pot. Stir in the chicken and sauce mixture and 1/2 cup of the shredded mozzarella.
Spoon the combined mixture into a 2-quart casserole dish or 8-inch square baking dish.
Bake in the preheated oven 20 minutes, then sprinkle the remaining mozzarella and the Parmesan over the top.
Return to the oven and bake an additional 3 minutes, or until the mozzarella has melted; serve warm.
