In a heavy pot, heat the oil. Fry the garlic and sliced onions over a low-medium flame for 6-7 minutes.
Add in the cauliflower florets and let it saute for around 15 minutes on a low flame. Don't let them brown if you want a white coloured soup.
Add 500 ml water / vegetable stock / water + veg stock cube. Bring to a simmer. Cover and simmer for 10 minutes until the cauliflower is completely softened.
Let it cool. Trasnfer to a blender, add the milk and blend to get a very fine puree.
Pour the puree into a saucepan. Simmer the soup for a few minutes to bring up the temperature. Season with more salt (if needed) and freshly ground black pepper and dried basil.
Serve hot in pre-heated bowls with some croutons or buttery garlic bread.