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To make the buns, put the flour in the bowl of a stand mixer fitted with a dough hook. Add the chives and salt on one side of the bowl, and the sugar and yeast to the other. Mix each side into the flour with your hands, then mix everything together using the dough hook. Tip the milk into a small pan and warm over a low heat until warm to the touch, but not hot. Slowly mix into the dry ingredients until combined. Lightly beat 3 of the eggs. With the motor on medium speed, slowly add the beaten egg and mix for 10 mins, then add the butter, one or two cubes at a time, until combined – this will take another 5-8 mins. Scrape the sides of the bowl down. The dough will be very soft at this stage.
Scrape the dough into a large bowl, cover with a clean tea towel, and leave to prove for 1 hr 30 mins-2 hrs until doubled in size. Once the dough has risen, chill for 1 hr.
Put the salmon, soft cheese and mustard in a food processor and pulse several times until the salmon is coarsely chopped. Transfer to a bowl and stir in half the capers, the dill and the lemon zest and juice. Season, then chill until needed.
Line a large baking sheet with baking parchment. Tip the dough out onto a lightly floured work surface, and divide into 18 equal-sized balls (weigh for accuracy, if you like). Butter the outside of a 12cm ovenproof bowl. Place the bowl in the middle of the baking sheet and arrange the dough balls around it, leaving a 2cm space between each for spreading. Cover with a tea towel and leave in a warm place to prove for 30-35 mins until doubled in size.
Heat the oven to 180C/160C fan/gas 4. Beat the remaining egg, then lightly brush it over the dough balls. Bake for 25-30 mins until golden and risen. Leave to cool on the sheet for 20 mins, then carefully remove the bowl (you may need to run a knife around it to release it). Spoon the pâté into a small bowl, place it in the gap in the middle of the buns, then top with extra dill, a grinding of black pepper and a drizzle of olive oil. To serve, tear the buns from the ring and spread with the pâté.
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