How to Make It
In a large saucepan, bring the water to a boil. Meanwhile, in a medium skillet, melt the duck fat over moderately low heat. Add the garlic, onion and shallots and stir to coat thoroughly with duck fat. Cook, stirring frequently, until the vegetables are thoroughly softened but not browned, about 12 minutes; if the garlic begins to brown, turn down the heat. Stir in the flour and cook gently for 5 minutes, stirring frequently; again, take care not to let the vegetables brown.
Season the boiling water generously with salt and pepper. Stir in the vegetables and simmer for 35 minutes. Transfer the hot soup to a blender and puree, in batches if necessary. Return the soup to the saucepan.
In a small bowl, beat the egg yolks with 1 tablespoon of the vinegar. Whisk a few tablespoons of hot soup into the egg yolks to warm them, then whisk the yolks into the soup. Whisk the soup over moderately low heat just until it begins to look creamy; do not let the soup boil or the eggs will curdle. Season the soup with salt and pepper and add a little more vinegar if desired. Ladle the hot soup into bowls, garnish with the toasted bread and the chives and serve.