Make the hollandaise sauce. Put the egg yolk into the small bowl of a food processor or a blender and season well with salt and pepper. Heat the lemon juice and vinegar in a small pan until just boiling. Switch on the processor and gradually add the vinegar mixture in a steady stream. Melt the butter in the pan and, with the processor switched on again, add this in a steady stream to give a smooth sauce.
Bring a large frying pan of water to the boil, then turn down the heat to a bare simmer. Break the eggs into the water and allow to cook very gently for 2 minutes. Remove from the pan with a slotted spoon.
Butter the muffins and top with the ham, a poached egg and a generous dollop of the sauce.