Peel and, using a mandolin, thinly slice the beetroot into 1 mm (1/32 inch) thick slices. Select the best 24 slices and place in a heatproof bowl. Place the vinegars, coriander seeds, bay leaves, sugar, salt, peppercorns and 75 ml (2⅔ fl oz) water in a saucepan and bring to the boil. Pour over the beetroot, cover with plastic wrap and refrigerate for 3 hours to pickle.
Dice the smoked salmon into 5 mm (¼ inch) cubes and combine with the créme fraîche, horseradish and dill.
Drain the beetroot, discarding the liquid. Place half of the slices on a work surface and place a teaspoon of the salmon mixture in the centre of each slice. Top with the remaining slices. Using the blunt edge of a 3 cm (1¼ inch) round cutter, make an indent around the filling without cutting all the way through. Using a 5 cm (2 inch) round cutter, cut out rounds from the beetroot slices and discard the trimmings. Set aside.
These can be made 1 day in advance and stored in an airtight container in the fridge.