Warm 3 tablespoons of the olive oil in a large stockpot over medium heat. Add the chopped onions, carrots and celery, tomato paste and a pinch of salt. Cook, stirring often, 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 and fresh ground black pepper.
Raise heat to medium-high and bring the mixture to a boil, then reduce heat and simmer. Cook for 15 minutes, then remove the lid and add the pasta, beans and greens. Continue simmering, uncovered, for 20 minutes.
Remove the pot from the heat; remove the bay leaves. Stir in the lemon juice and remaining tablespoon of olive oil. Taste and season with more salt and pepper. Garnish bowls of soup with Parmesan, if you’d like.