Melt butter in a large saucepan. Add onion; sauté 10 minutes or until tender. Add broth, potatoes, parsley, mustard, salt, and pepper; cook over low heat 30 minutes or until potatoes are tender.
Combine potato mixture and cucumber in container of an electric blender; process 3 to 4 minutes or until pureed. Chill at least 4 hours.
Stir in half-and-half before serving; garnish with cucumber slices.