Warm 3 tablespoons of the olive oil in a large Dutch oven or stockpot over medium heat. Once the oil is shimmering, add the chopped onion, carrot, celery, tomato paste, and a pinch of salt. Cook, stirring often until the vegetables have softened and the onions turn translucent about 7 to 10 minutes.
Add the seasonal vegetables, garlic, oregano, and thyme. Cook until fragrant while stirring frequently, about 2 minutes.
Pour in the diced tomatoes and their juices, broth, and water. Add the salt, bay leaves, and red pepper flakes. Season generously with freshly ground black pepper.
Raise heat to medium-high and bring the mixture to a boil, then partially cover the pot with the lid, leaving about a 1” gap for steam to escape. Reduce heat as necessary to maintain a gentle simmer.
Cook for 15 minutes, then remove the lid and add the pasta, beans, and greens. Continue simmering, uncovered, for 20 minutes or until the pasta is cooked al dente and the greens are tender.
Remove the pot from the heat, then remove the bay leaves. Stir in the lemon juice and the remaining tablespoon of olive oil. Taste and season with more salt and pepper. We love this with warm bread slathered with olive oil! Garnish bowls of soup with grated Parmesan.