Heat the olive oil in a large pot over medium heat. Add the chopped onion and garlic and cook until the onion is translucent, about 5 minutes.
Add the diced carrots, celery, zucchini, and potato to the pot. Cook for an additional 5 minutes, stirring occasionally.
Pour in the can of diced tomatoes (with their juices) and the vegetable broth. Bring the mixture to a boil.
Once boiling, reduce the heat to a simmer and add the rinsed and drained kidney beans. Let the soup simmer for 20 minutes.
Add the small pasta to the pot and continue to simmer for another 10 minutes, or until the pasta is tender.
Stir in the chopped spinach and Italian seasoning. Season the soup with salt and black pepper to taste.
Serve the Minestrone Soup hot, garnished with grated Parmesan cheese if desired.