Chilled and Dilled Avgolemono Soup

Simmer stock and rice in a heavy medium saucepan, covered, until rice is very tender, about 30 minutes. Purée mixture in a blender (use caution when blending hot liquids). Whisk eggs together in a medium bowl. Gradually whisk in hot stock mixture. Return to saucepan and cook over medium heat, stirring constantly with a wooden spoon, until soup registers 170 °F on an instant-read thermometer. Strain soup through a fine-mesh sieve into a metal bowl. Stir in lemon juice, then quick-chill in an ice bath, stirring occasionally, until cold. Stir in scallion, dill, and salt and pepper to taste.