Heat olive oil in a large, heavy-bottomed pot over medium heat. Add the diced onion, carrots, and celery, cooking for about 5-7 minutes until the vegetables soften and the onion is translucent.
Stir in minced garlic and cook for another minute, being careful not to brown it.
Pour in chicken broth and nestle the chicken breast into the pot. Add bay leaves, oregano, thyme, and red pepper flakes if using.
Bring to a gentle boil, then reduce heat to a simmer. Cover partially and cook for 25-30 minutes until the chicken is cooked through and shreds easily.
Remove chicken and set aside to cool. Season broth with salt and pepper.
Shred the chicken, discarding skin and bones. Return shredded chicken to the pot.
Bring soup back to a gentle boil and add pasta. Cook according to package directions until al dente.
Remove bay leaves and stir in fresh lemon juice and chopped parsley. Adjust seasoning as needed.
Serve topped with freshly grated Parmigiano-Reggiano cheese and a drizzle of extra virgin olive oil with crusty Italian bread on the side.