Heat the olive oil in a large pot or deep skillet over medium heat, then add the minced garlic and cook for 1 minute until fragrant.
Add the pasta, chicken broth, Italian seasoning, and black pepper to the pot and bring to a boil.
Reduce heat to medium and simmer for 12-15 minutes, stirring frequently, until the pasta is nearly tender.
Add the cream cheese cubes and stir continuously until melted and incorporated into the sauce.
Stir in the cooked chicken, spinach, mozzarella, and Parmesan cheese, cooking for 2-3 minutes until the spinach is wilted and the cheese is melted.
Remove from heat and let stand for 2 minutes to allow the sauce to thicken before serving.