Cut the carrot, the potato, the mushrooms and the onion into small pieces.
Heat a big soup pot and melt the butter.
Add the onion and the garlic and cook over low heat for a couple minutes.
Add the potatoes, the carrots, and the mushrooms and cook for 5 minutes until the mushrooms lose a bit of water.
Add the water, the vegetable broth, and the frozen clams and let it simmer for about 15 minutes (until the carrots and the potatoes are fork-tender).
Pour the milk and season with salt and pepper to taste. Cook for a couple minutes.
Serve and sprinkle with chives.