Rinse the potatoes in cold water and then put them in a saucepan containing
Cut away the bottom half of the watercress stalks, rinse the remainder in cold water, then spin-dry. Heat a large, heavy saucepan until very hot. Throw in one-quarter of the butter, then quickly follow with the watercress to prevent the butter burning. Season with a pinch of salt and, as soon as the watercress has wilted, add the potatoes and their water. Bring back to the boil, then turn the heat down and simmer for 2 minutes. Blend the soup until it is a deep green colour with no flecks remaining.
Melt the remaining butter in a frying pan and add the cubes of bread. On a high heat, turn the croutons constantly as they cook, shaking the pan and turning them with a slotted spoon so they colour evenly. Once they turn an even golden brown, drain them, saving the butter.
Bring a deep saucepan of water to a simmer. Add a capful of wine vinegar. Carefully break each egg into a cup. Gently reheat the soup without letting it boil and have six warm bowls at the ready. Bring the water back to the boil and slip one of the eggs into its fastest eddy. The water will slow down until the egg comes back to the surface. Each time the water comes back to the boil, repeat the process. Turn the heat down and let the eggs gently poach, keeping them nicely runny in the middle. As soon as they are cooked, lift them out with a slotted spoon, trimming off any trailing white.
To serve, pour the very hot soup into bowls, slip in an egg and sprinkle a few croutons on top. A teaspoon of the butter can be poured over each egg.