Vichyssoise is a classic French potato-and-leek soup. Hollowed-out cucumber cups hold just enough of the creamy puree for everyone to have a taste.
Melt butter in a medium saucepan over medium heat. Add leeks and cook, stirring often, until tender, about 10 minutes. Add potatoes and stock. Season with salt. Simmer until potatoes are tender, about 30 minutes.
Strain leek-potato mixture through a fine sieve, reserving liquid. Puree solids in a food mill or blender, adding reserved liquid as needed, just until smooth. Stir in remaining reserved liquid.
Strain soup through sieve into a large bowl, and stir in half-and-half and nutmeg. Season with salt and white pepper. Refrigerate vichyssoise until chilled, about 1 hour.
Meanwhile, hollow out cucumbers using a melon baller, leaving bottoms intact. Refrigerate, covered with a damp towel, until ready to use.
Stir cream into chilled vichyssoise just before serving. Fill cucumber cups with vichyssoise and garnish with chives.
Vichyssoise can be refrigerated for up to 3 days at the end of step 2. Cucumber cups can be refrigerated, covered, for up to 4 hours.