First make the sauce. Whisk the egg yolks, mustard and yogurt in a heatproof bowl set over a large saucepan of simmering water (without letting the bowl touch the water) for about 10 minutes until thick, then remove from the heat. Add the chives and season to taste. Cover the bowl to keep the sauce warm.
Heat the oil in the pan, add the spinach and stir-fry over a medium heat for 2–3 minutes until wilted. Drain in a sieve, pressing down with the back of a spoon to remove excess moisture. Season to taste, then cover to keep warm.
To poach the eggs, fill the pan one-third with water. Add the vinegar and a pinch of salt and heat to simmering. Carefully break in the eggs, one at a time, and cook gently for 2–3 minutes until cooked as you like them, spooning the hot water over the yolks towards the end of the cooking time. Meanwhile, toast the muffins. Using a spatula or slotted spoon, lift the eggs from the water one at a time and drain on paper towel.
Divide the spinach among the muffin bases, place a poached egg on top and spoon over the warm sauce. Garnish with whole chives, if you like, sprinkle with pepper and rest the remaining toasted muffin halves on the side.