• Bring a deep saucepan of water to the boil (at least 2 litres) and add the vinegar. Break the eggs into 4 separate coffee cups or ramekins. Split the muffins, toast them and warm some plates.
• Swirl the vinegared water briskly to form a vortex and slide in an egg. It will curl round and set to a neat round shape. Cook for 2-3 mins, then remove with a slotted spoon.
• Repeat with the other eggs, one at a time, re-swirling the water as you slide in the eggs. 

Make hollandaise sauce

• Melt the butter in a saucepan. Skim any white solids from the surface. Keep the butter warm.
• Put the egg yolks, white wine or tarragon vinegar, a pinch of salt and a splash of ice-cold water in a metal or glass bowl that will fit over a small pan. Whisk for a few minutes, then put the bowl over a pan of barely simmering water and whisk continuously until pale and thick, about 3-5 mins.
• Remove from the heat and slowly whisk in the melted butter bit by bit until it’s all incorporated and you have a creamy hollandaise. (If it gets too thick, add a splash of water.) Season with a squeeze of lemon juice and a little cayenne pepper. Keep warm until needed.
• Spread some sauce on each muffin, scrunch a slice of ham on top, then top with an egg. Spoon over the remaining hollandaise and serve at once.