Preheat the oven to 180°C.
First, make the crispy potato cakes. Melt the butter and use a little to grease a standard Yorkshire pudding tin.
Grate the potatoes and in a tea towel squeeze out as much liquid as you can. Place the potatoes in a bowl and pour over the rest of the melted butter. Season to taste and mix until well combined. Using two forks, divide the mixture among the Yorkshire pudding moulds, gently pressing it in. Bake for 20- 25 minutes or until crisp and golden brown, flipping halfway through.
Meanwhile, heat a large sauté pan with water. Add the white wine vinegar and salt then bring to the boil. Break each egg into the water where it is bubbling, then reduce the heat and simmer gently for 3 minutes, until the eggs are just cooked through but the yolks are still soft. Remove with a slotted spoon and plunge into a bowl of iced water.
When ready to serve, make the asparagus curls. Using a potato peeler, pare the asparagus into curls and place it in a bowl. Toss in the olive oil to lightly coat and season with salt and some lemon juice.
To make the butter sauce, melt the butter in a small saucepan. Continue to cook over a medium-high heat until it turns a nutty golden brown. Whisk in the lemon juice and chives and serve over the top of the salmon.
Return the sauté pan filled with water to the boil. Add the poached eggs and cook for 1 minute to warm through.
Run a small palette knife around each crispy potato cake to loosen them and put one onto each warmed plate. Arrange the smoked salmon flakes on top. Drain the poached eggs briefly on kitchen paper and then place one on each serving. Spoon over the beure noissette and garnish with a good grinding of black pepper. Finish with the asparagus curls and serve straight away.