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Melt butter in soup pot over medium heat. Add leeks and sauté until limp (about 5 minutes).
Add potatoes and broth. Bring to a boil, reduce heat, cover and simmer 15 minutes, stirring occasionally.
Remove from heat. Purée soup in blender, then add milk and pepper (and salt to taste). Mix thouroughly. Serve.
Makes 6 servings.