Warm the oil in a pot over medium heat, and cook the leeks for a few minutes. Add the green beans and cook for 5 minutes, stirring occasionally. Add the broccoli, zucchini and vegetable stock. Bring to a boil, then reduce the heat and simmer for 20 to 25 minutes. When the vegetables are tender, put through a vegetable mill.

Return the milled vegetables to the pot. Season with salt and pepper to taste, add the milk and cook, stirring, over medium heat for 10 minutes more. Sprinkle with parsley, and serve.