Begin by thoroughly washing the leeks to remove any dirt between the layers. Trim the roots and the dark green parts. Slice the leeks into thin rounds.
Peel the potatoes and cut them into small cubes (about 1 inch each).
Chop the onion into small pieces.
In a large pot, heat the olive oil over medium heat. Add the chopped onions and sauté until they become translucent, about 5 minutes.
Add the sliced leeks to the pot and cook for an additional 5 minutes, stirring occasionally, until softened.
Stir in the cubed potatoes, salt, and pepper. Mix everything together and cook for another 2 minutes.
Pour in the vegetable broth and bring the mixture to a boil. Once boiling, reduce the heat to low and cover the pot. Let it simmer for about 20 minutes or until the potatoes are tender.
Once cooked, carefully blend the soup using an immersion blender until smooth. Alternatively, you can transfer the soup in batches to a regular blender. If using a blender, be cautious with the hot liquid.
If desired, stir in the heavy cream for added richness. Taste and adjust seasoning if necessary.
Serve the soup hot, garnished with fresh parsley.