Melt in a soup pot over medium-low heat:
Add and cook, stirring, until very tender but not browned, about 20 minutes:
Stir in:
Bring to a boil, then reduce the heat, partially cover, and simmer until the potatoes are soft, about 25 minutes. Puree the soup with an immersion blender (or in batches in a food processor or regular blender) until smooth. For a finer texture, you may push through a chinois or fine-mesh sieve. Return to the pot and warm through if necessary. Season to taste with:
Thin, if necessary, with: