To make the eggs: add the vinegar to a small pan of just simmering water and swirl it rapidly. Crack the eggs carefully into the centre of the swirling vinegar. Put a lid on the saucepan and leave for 3 minutes until the whites become solid. Lift out with a slotted spoon and leave to drain on each plate.
For the Hollandaise: Place the egg yolks into a food processor with some salt and blend until well combined. In a saucepan, gently heat the lemon and vinegar together in a small pan and pour into the egg yolk mixture while continuing to blend.
On a gentle heat, melt the butter. Then slowly drizzle the butter into the egg mixture while still blending until it forms a creamy sauce. Place two slices of ham over each toasted muffin half and top with the poached eggs. Pour the hollandaise sauce over the eggs and serve.