Melt butter in a large pot over medium heat. Add leeks and cook until softened, about 5-7 minutes.

Add potatoes and vegetable broth to the pot. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 15-20 minutes.

Carefully blend the soup using an immersion blender or transfer to a regular blender. Blend until smooth and creamy.

Stir in heavy cream, salt, and pepper. Heat through gently.

Serve hot.