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