This dish traditionally uses ham or bacon and a rich butter sauce. Here, a yogurt and chive hollandaise sauce contrasts with the richness of poached eggs and lean ham, to make a lighter, but equally special version.
To make the hollandaise sauce, whisk together the egg yolks, mustard and yogurt in a heatproof bowl. Set over a saucepan of barely simmering water and cook for about 12–15 minutes, stirring constantly, until thick – the sauce will become thinner at first, but will then start to thicken. Stir in the chives, and season with pepper. Remove from the heat and keep the sauce warm over the pan of hot water.
Half-fill a frying pan with water. Bring to a boil, then add the vinegar. Reduce the heat so the water is just simmering gently, then carefully break the eggs into the water, one at a time. Poach for 3–4 minutes, spooning the hot water over the yolks towards the end of cooking.
Meanwhile, preheat the grill to high. Lightly toast the muffin halves for about 1 minute on each side. Place one half on each of four warmed plates and top each with a slice of Parma ham, crumpled slightly to fit. Season with pepper.
Using a slotted spoon, remove the poached eggs from the pan, one at a time. Drain on kitchen paper and, if liked, trim off any ragged edges of egg white with scissors. Place an egg on each ham-topped muffin half.
Spoon the warm hollandaise sauce over the eggs, and sprinkle each serving with a pinch of paprika and the chives. Serve immediately with the remaining toasted muffin halves. Instead of chives, add 1 tablespoon chopped fresh tarragon to the hollandaise, and garnish with sprigs of tarragon.