Heat the olive oil in a 4 to 5 quart Dutch oven or stock pot over medium heat, until the oil shimmers. Add the onions, celery, and carrots, and saute until soft, 8 to 10 minutes. Add the garlic, and stir until fragrant (just a minute or two). Sprinkle the flour over the vegetables and cook until its disappeared into the vegetables.
Add the chicken broth, marinara, pasta, cheese rind (if using), bay leaf, and Italian seasoning, and stir until mixed well.
Increase heat to medium-high and bring soup to a gentle boil, then reduce heat to maintain an active simmer. Cover pot partially with a lid and let simmer for 15 minutes. Test a piece of the pasta to make sure it's done to at least al dente. Remove and discard the bay leaf and parm rind. Taste the soup and add salt and pepper as needed.
Stir in the cooked chicken. Place mozzarella slices over the top of the soup (optional: place the soup under the broiler and heat until the cheese bubbles - make sure you're using a broiler-safe pot).
Sprinkle grated cheese and parsley over the soup, and serve.