Start by cleaning the leeks thoroughly, cutting off the dark green tops, slicing them in half lengthwise, rinsing under cold water, and chopping into thin slices.
In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes until they become translucent.
Add the sliced leeks and diced potatoes to the pot. Sauté for another 5 minutes, stirring occasionally.
Pour in the vegetable broth and bring the mixture to a boil.
Once boiling, reduce the heat to low and cover the pot. Simmer for about 20 minutes or until the potatoes are tender.
Remove the pot from the heat. Use an immersion blender to puree the soup until smooth. If using a regular blender, carefully transfer the soup in batches and blend until smooth.
Return the soup to the pot. If desired, stir in the heavy cream for a creamier texture. Season with salt and black pepper to taste.
Heat the soup gently on low until warmed through, then serve hot. Garnish with fresh chives or parsley if desired.