Heat the olive oil in a large, heavy bottomed saucepan over medium heat, then add the chopped onion, leek celery and carrots, stirring well, and cook for a couple of minutes to allow the flavors of the vegetables to release.
Stir in the chopped tomatoes, and the garlic. Cover and simmer for 15 minutes, checking and stirring often. Pour in the vegetable stock, then add the cabbage, herbs, and the bay leaf, and mix in the tomato paste. Bring to a boil, reduce the heat, and let it simmer for 15 minutes.
Add the frozen peas, or fava beans and pasta and continue to simmer gently for a further 15 minutes. Add more stock if its' too thick. Taste, and season with sea salt (only if it needs it, as the stock may be salty enough) and ground black pepper. Ladle generously into soup bowls and sprinkle grated Parmesan cheese over the top.