Rinse the leek thoroughly and chop finely. Divide the rest of the broccoli into smaller florets.
Place the leek and the sliced broccoli core in a pot and cover with water. Season with salt, and bring to a boil for a few minutes on high heat.
Add the florets and vegetable stock cube, lower the heat and simmer for a few minutes, until the broccoli is bright green and tender.
Add the rest of the ingredients. Blend with an immersion blender until desired consistency.
If the soup is too thick, thin it out with water. If you’d like it to have a slightly thicker consistency, add a touch of heavy cream.