Heat a large heavy-bottomed pot over medium heat and add a splash of olive oil, swirling to coat the bottom.
Add chopped onions, carrots, and celery to the pot. Sauté until the vegetables soften and release a sweet aroma, about 8 minutes, stirring occasionally.
Stir in minced garlic and cook for another minute until fragrant, taking care not to let it burn.
Pour in chicken broth and bring to a gentle simmer, then add shredded cooked chicken and season with salt, pepper, and red pepper flakes.
Stir in the pasta and cook until al dente, about 10 minutes, until the soup thickens slightly and flavors meld.
Taste the soup and adjust seasoning as needed. Squeeze in fresh lemon juice and stir in chopped parsley for brightness.
Ladle the hot soup into bowls, garnish with additional herbs if desired, and serve immediately while steaming hot.