Step 1

Heat oil in a large saucepan or small pot over medium. Add onion and celery, season with salt, and cook, stirring occasionally, until onion is translucent but not developing color, about 5 minutes. Add garlic; cook 1 minute more. Add broth, 2 cups water, lemon zest, and rice. Bring to a boil, then reduce heat to low, cover, and simmer until rice is tender, 15 to 18 minutes. Remove from heat.

Step 2

In a blender, purée egg, yolks, and lemon juice until pale and doubled in volume, 2 to 3 minutes. Reduce speed to lowest setting; remove feed-tube cap from lid. Slowly and carefully ladle about 2 cups of soup into blender (be sure to include a combination of broth and rice). Return cap to blender lid, increase speed to high, and blend until very smooth and frothy.

Step 3

Generously season fish with salt and pepper. Add to soup and simmer over medium-low heat just until fish is cooked through, about 5 minutes. Stir egg mixture into soup, breaking up fish into bite-size pieces. Season and add more lemon juice to taste, 1 teaspoon at a time. Serve topped with herbs and a drizzle of oil.