Thoroughly clean the leeks: Leeks can contain sand, so slice them lengthwise and rinse under cold water to eliminate any grit.

Peel and dice the potatoes: Cut them into uniform pieces to ensure even cooking.

Sauté the leeks: Melt butter in a large pot over medium heat. Add the leeks and cook gently until they are soft but not browned, about 5-7 minutes.

Add potatoes and broth: Pour in the broth and bring to a boil. Lower the heat and simmer until the potatoes are tender, roughly 20 minutes.

Blend the soup: Use an immersion blender or transfer the soup to a blender in batches. Blend until it is smooth and creamy.

Season and finish: Add salt, pepper, and cream if desired. Heat through without boiling.