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