Heat a large heavy-bottomed pot over medium heat and add the olive oil. Let it shimmer for about 2-3 minutes.
Add the chopped onion, carrots, and celery to the pot. Cook, stirring occasionally, until the vegetables are soft and fragrant, about 8 minutes.
Stir in the minced garlic and cook for an additional 30 seconds until fragrant, being careful not to burn it.
Pour in the chicken broth and bring the mixture to a gentle simmer. Add the shredded cooked chicken, bay leaf, and pasta to the pot.
Cook until the pasta is tender, about 10 minutes, stirring occasionally and checking for doneness.
Remove the bay leaf, then stir in the fresh lemon juice, chopped parsley, and a splash of olive oil. Let the soup sit off the heat for 5 minutes to meld the flavors.
Taste the soup and adjust the seasoning with salt and pepper as needed.
Serve the soup hot, garnished with additional herbs and a lemon wedge if desired.
