To make the hollandaise sauce, bring a small saucepan of water to a gentle simmer. Find a heatproof glass bowl that will fit neatly on top without touching the water and add the yolks, vinegar and 1 teaspoon of lemon juice. Whisk together until frothy, then place the bowl over the simmering water and whisk again until the mixture thickens.
Gradually whisk in the butter, starting with single cubes, and as the sauce gets thicker, add 2–3 at a time. If the sauce begins to look oily – as if it might be splitting – whisk the mixture off the heat for a few minutes. When all the butter is incorporated, season with the remaining lemon juice, salt and white pepper.
Turn off the heat but leave the bowl on top to keep the sauce warm. A piece of greaseproof paper laid directly on the surface will stop a skin forming.
To poach the eggs, fill a saucepan with 10cm/4in of water and a splash of white wine vinegar. Bring to a gentle simmer. Fill a large bowl with cold water. Crack the first egg into a small sieve – this will drain away any runny egg that might cloud the water.
Lower the heat so just a few small bubbles remain then stir to create a whirlpool. When the whirlpool has almost disappeared, tip the egg from the sieve into the middle of where the whirlpool was. Poach for 2 minutes while watching the heat – there should be small, gentle bubbles constantly but nothing more vigorous.
Spoon the poached egg into the cold water. Repeat 3 times and keep the water gently simmering when all the eggs are done.
Top each muffin half with a slice of smoked salmon. Reheat all the eggs in the poaching pan for 30 seconds, then sit on top of the salmon. Give the sauce a quick stir then spoon over the top of each egg – if it’s too thick, stir in a splash of cool water to thin. Garnish with the chives and serve immediately.
