Heat oil in a large Dutch oven or pot over medium. Add onion, garlic, celery, salt, black pepper, and 1¼ cups carrots; cook, stirring occasionally, until vegetables are starting to soften, about 8 minutes.
Stir in chicken broth, thyme, oregano, bay leaf, and Parmesan rind, if using. Bring to a boil over medium-high. Reduce heat to medium-low and simmer, stirring occasionally, until vegetables are tender, about 10 minutes. Discard thyme sprigs, oregano sprigs, bay leaf, and Parmesan rind (softened rind can be chopped and eaten if desired).
Transfer vegetables to a blender using a slotted spoon. Pour in ½ cup broth. Secure lid on blender and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 45 seconds.
Return vegetable mixture to Dutch oven. Bring soup to a boil over medium-high. Stir in acini di pepe pasta and remaining 1 cup carrots. Reduce heat to medium-low and simmer, stirring often and scraping bottom of Dutch oven, until pasta and carrots are tender, about 12 minutes. Stir in shredded chicken and cook, stirring occasionally, until warmed through, about 3 minutes.
Remove from heat and stir in lemon juice. Divide evenly among 4 bowls, and garnish with grated Parmesan cheese, olive oil, black pepper, and parsley. Serve immediately.