Heat 3 tbsp olive oil in a large pot over medium heat. Add onion, carrot, celery, tomato paste, and a pinch of salt. Cook for 7–10 minutes until soft.
Add garlic, oregano, thyme, and seasonal vegetables. Cook for 2 minutes until fragrant.
Pour in diced tomatoes with juices, broth, and water. Add salt, bay leaves, and red pepper flakes. Season with black pepper.
Bring to a boil over medium-high heat, then partially cover the pot. Reduce heat and simmer gently.
Cook for 15 minutes, then add pasta, beans, and greens. Simmer uncovered for 20 minutes until pasta is al dente and greens are tender.
Remove from heat and take out the bay leaves.
Stir in lemon juice and remaining 1 tbsp olive oil. Adjust salt and pepper to taste.
Serve hot, garnished with grated Parmesan if desired.