In a large stockpot, bring the chicken broth, lemon juice, bay leaf, and Parmesan rind, if using, to a boil over medium-high heat. Add the carrots and simmer until tender, about 5 to 8 minutes. Add the pasta and cook until the pasta is tender, for 4 to 5 minutes, stirring occasionally. Add the chicken and heat through, about 2 to 3 minutes. Remove the bay leaf and the Parmesan rind and discard. Stir in 1/2 of the cheese and the parsley. Season with salt, to taste. Ladle the soup into serving bowls and sprinkle with the remaining cheese.