Heat a large pan with 2.25 litres water. Add the white wine vinegar and bring to the boil. Break each egg into the water where it’s bubbling, then move the pan to the edge of the heat and simmer gently for 3 minutes. Remove the poached eggs with a slotted spoon and plunge into a bowl of iced water. When cold, trim down any ragged ends from the cooked egg white. These will keep happily in the fridge for up to 2 days.
When ready to serve, preheat the grill. Add half of the butter to a large pan on a fairly high heat, and once it starts to foam, tip in the spinach and sauté until wilted. Season with a pinch of salt and plenty of pepper and drain off any excess liquid. Keep warm.
Arrange the muffin halves on a grill pan, cut side up, and cook for 2–3 minutes, until lightly toasted. Spread with the rest of the butter.
Meanwhile, bring a large pan of water to the boil. Add the poached eggs and cook for 1–2 minutes to warm them through.
To make the sauce, place the cream and mustard in a small pan and simmer for 1 minute. Whisk in the butter and stir in the tarragon. Season with a pinch of salt and plenty of pepper. Place the muffins on warmed plates and then cover with small mounds of the drained spinach. Using a slotted spoon, remove the poached eggs from the pan and drain briefly on kitchen paper. Place on top of the spinach and spoon over the tarragon sauce to serve.