Place a heavy-bottom stock pot on the stove over medium heat. Chop the vegetables while it heats up.
Add the olive oil to the pot and allow to warm. Place the onion, carrot, and celery in the pot and sauté for 5 minutes until soft, stirring occasionally. Add the garlic and cook for 1 additional minute.
Add the potato, zucchini, tomatoes, broth, spices, wine and bay leaf if using. Stir to combine everything and bring the pot to a boil. Once boiling, reduce the heat to low and simmer. Place a lid partially covering the pot so that steam can escape. Simmer for 30 minutes.
While the soup is simmering, cook the pasta in a separate small pot of salted water. Gluten-free pasta releases a lot of starch, so cooking it in a separate pot will help remove the starchy water, and also avoid overcooking. Cook pasta according to the package instructions, but cook about 2 minutes less than the stated time. Rinse pasta thoroughly in cold water to stop the cooking process. Set aside until the soup is almost finished.
When the soup has simmered for about 30 minutes, add the beans. Rip some fresh parsley and stir into the soup. Allow to simmer for 5-10 more minutes. Remove the bay leaf.
If you will be sharing and consuming all of the soup in one sitting, add the pasta to the pot. If you will not finish all the soup, add some pasta in each bowl. To serve, top soup with fresh parsley and parmesan cheese. Enjoy warm! See storage instructions below.