Peel onion and cut into small cubes. Rinse leeks and cut into 1 cm (approximately 1/2 inch) wide strips. Peel carrots and cut into slices. Peel potatoes and dice. Rinse celery, trim and cut into slices. Blanch tomatoes for a few seconds, rinse in cold water, peel, remove seeds and coarsely chop.
In a large pot, heat broth and add onions, potatoes, carrots and celery. Simmer for 10 minutes and then reduce heat. Add noodles and remaining vegetables and cook according to the package directions. Season with salt and pepper. To serve, distribute the minestrone in soup bowls and garnish with Parmesan cheese and basil.