Heat oil in a large, high-sided skillet or Dutch oven over medium-high heat. Add chicken; cook, stirring often to break up the meat, until cooked through and beginning to brown, 6 to 8 minutes. Add onion, tomatoes, Italian seasoning and salt; cook, stirring often, until the onion is softened and the tomatoes are breaking down, 4 to 5 minutes.
Stir in pasta, broth, marinara and cream; bring to a simmer over medium-high heat. Cover and simmer, stirring occasionally, until the pasta is al dente, 10 to 12 minutes. Stir in spinach (in batches, if necessary), basil and mozzarella; cover and cook until the spinach wilts and the cheese melts, about 2 minutes. Garnish with more basil and Parmesan, if using.
