Wash the leeks and discard the green ends. Finely slice the white part of the leeks and dice the potatoes into small cubes.
Heat the olive oil in a large sauce pan over medium heat and add the leeks and garlic. Cook for 2-3 minutes and then add the potatoes. Cook for a further 5 minutes, stirring regularly to ensure nothing sticks to the pot.
Add the vegetable stock into the sauce pan and bring to a simmer, cover and turn the heat down, simmer for 15 minutes or until the potatoes and leeks have softened considerably.
Blend the soup with an immersion blender and season with salt and pepper to taste.