Preheat your oven to 375 degrees Fahrenheit and lightly grease a 9x13 inch baking dish.
Boil a large pot of salted water and cook the pasta according to package instructions until al dente, then drain and set aside.
In a large skillet, heat olive oil over medium-high heat, add the diced chicken, and cook until browned and fully cooked through.
Lower the heat to medium, add the minced garlic to the chicken, and sauté for 1 minute until fragrant.
Stir the heavy cream and basil pesto into the skillet, letting the sauce simmer for 2 to 3 minutes until it begins to thicken.
Fold in the fresh spinach and cook for another minute until wilted, then remove the skillet from the heat.
Combine the cooked pasta with the creamy pesto chicken mixture and mix well to coat all the noodles.
Pour the mixture evenly into the prepared baking dish and sprinkle the shredded mozzarella and grated parmesan cheese on top.
Bake uncovered for 15 to 20 minutes until the cheese is melted, bubbly, and slightly golden.
Garnish with fresh chopped parsley and let it rest for 5 minutes before serving.