Melt butter in a large pot over medium heat. Cook and stir leeks in the melted butter until softened, about 15 minutes.
Stir in chicken stock and potatoes and bring to a boil. Reduce heat and simmer until potatoes are tender, about 20 minutes.
Pour about half of the soup into a blender, filling the pitcher no more than halfway full. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to puree. Pour the pureed soup back into the pot.
Stir in heavy cream and season with sea salt and black pepper.