First of all, put your potato in a pot with water, bring to a boil, and cook until tender, for about 30 minutes.
Meanwhile, prepare all the veggies. When the potato is cooked, heat 3 tablespoons olive oil in a soup pot over medium-high heat, and cook the onion, carrot, celery, and garlic for about 5 minutes, until the veggies start to brown.
Discard the garlic cloves. Add the tomatoes and cook for 5 minutes more. Add ⅔ of the beans (should be about 2 cups), season, and cook for about a minute. Add the water or the vegetable broth. Peel the potato and mash it together with the remaining ⅓ of the beans with a fork or any tool you like and add to the pot. Add the bay leaf, and bring the soup to a boil. Lower the heat, cover, and cook for 15 minutes.
Add the pasta and cook until it's done. Stir in the parsley and serve. Drizzle some of the remaining olive oil and sprinkle some Parmesan over each bowl. Enjoy!