Pour in the vegetable broth and add the diced potato. Bring to a boil, then reduce heat and simmer until the potatoes are tender, about 15 minutes.
Add the chopped butter lettuce to the pot and cook for another 5 minutes until wilted.
Remove the pot from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer the soup in batches to a blender and blend until smooth.
Return the soup to low heat and stir in the heavy cream. Season with salt and pepper to taste. Heat through but do not boil.
Serve hot, garnished with chopped chives.
Notes
For a lighter version, substitute half of the heavy cream with low-fat milk or a non-dairy alternative.
Add a squeeze of lemon juice before serving for a bright, fresh flavor.