Heat the oil in a heavy large pot over medium heat. Add the leeks and saute until translucent, about 8 minutes. Add the garlic and saute until tender, about 2 minutes. Stir in the zucchini and artichokes. Season the vegetables with salt and pepper. Saute until the zucchini are tender, about 10 minutes. Add the vegetable broth. Stir in the thyme and cook for 2 minutes. Cover the pot and bring the soup to a simmer. Decrease the heat to medium-low and simmer gently until the flavors develop, stirring occasionally, about 20 minutes. Increase the heat to medium-high. Add the noodles and cook until al dente, stirring constantly, about 5 minutes.
Ladle the soup into bowls. Sprinkle with Parmesan and serve.