Heat a little oil in a large saucepan over a medium heat. Add the roughly chopped leeks, onion, garlic and potato, then sauté for 5 to 6 minutes until softened.
Add the chopped cabbage and cook for a further 1 to 2 minutes, stirring occasionally.
Pour in 1300ml of water and bring to the boil. Reduce the heat and simmer for 10 minutes.
Add the roughly chopped broccoli, kale and edamame beans. Simmer for another 6 minutes until the vegetables are tender but still vibrant green.
Stir in the spinach and cook for 1 minute until wilted.
Carefully blend the soup in batches until completely smooth, then return it to the pan. Stir through the cream and season generously with salt and black pepper to taste.