Bring the stock to a simmer in a pan, then stir in the watercress and simmer for 1-2 minutes, or until the watercress is wilted. Blend until smooth with a stick blender and keep warm.
Bring a pan of water to the boil, then reduce to a gentle simmer and add the vinegar. Crack the egg into a bowl. Swirl the water with a wooden spoon to form a whirlpool, then pour the egg into the centre of the whirlpool. Poach for 2-3 minutes, or until the whites have just set, then remove with a slotted spoon and drain on kitchen paper.
To serve, ladle the soup into a serving bowl and place the poached egg on top. Garnish with a sprinkling of grated cheddar.