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First, make the hollandaise. Put the vinegar, shallots, dill (if using) and some cracked black pepper in a small pan, and bring to the boil. Reduce the heat and simmer for 5-6 mins until the mixture has reduced by two-thirds. Remove from the heat and leave to cool. Melt the butter in a second saucepan over a low-medium heat, then sizzle until it turns light brown. Turn the heat off and pour it into a small jug.
Fill a saucepan a third full with water, bring to the boil, then reduce the heat to a simmer. Strain the infused vinegar mixture through a sieve into a bowl, add the egg yolks and miso, and set the bowl over the pan of simmering water, ensuring the bowl doesn’t touch the water. Whisk continuously until the yolks lighten in colour – you should be able to see trails from the whisk. Whisk in the cream, then slowly pour in the melted butter, whisking continuously until fully incorporated. Season with salt, the cayenne and lemon juice to taste, then remove the bowl from the pan and cool to room temperature, stirring occasionally.
Heat the grill to high and toast the muffins cut-side up. Set aside and keep warm. Tip the vinegar into the pan of water on the hob, return to the boil, then reduce the heat to a simmer. If you’re confident, crack the eggs directly into the simmering water, or crack the eggs into individual cups or ramekins first and carefully slide the eggs into the water. Set a timer for 2 mins 30 seconds if the eggs were at room temperature, or 3 mins if they were from the fridge. When ready, the egg whites should be set and the yolk runny. Carefully lift the eggs out of the water using a slotted spoon, then drain on kitchen paper, trimming away any wispy bits of the whites, if you like.
Press your thumbs into the middle of the toasted side of each muffin to make a dip, then arrange the smoked salmon around the edge to create a kind of nest, leaving the dip in the middle free. Carefully nestle the poached eggs into the middle, then generously spoon over the hollandaise, season with black pepper and serve.