Cook the leeks: In a large pot, melt the butter over medium heat. Add the sliced leeks and cook until softened, about 5-7 minutes.

Add the broth: Pour in the chicken broth and bring the mixture to a boil. Reduce the heat and simmer for about 10-15 minutes until the leeks are very tender.

Blend the soup: Use an immersion blender to puree the soup until smooth. Alternatively, transfer the mixture to a blender in batches and blend until smooth.

Add the cream and cheddar: Stir in the heavy cream and shredded cheddar cheese. Continue stirring until the cheese is fully melted and the soup is creamy. Season with salt and pepper to taste.

Serve: Ladle the soup into bowls and garnish with fresh chives, if desired. Serve warm.