Place the salt, sugar, dill, caraway seeds and white peppercorns into a food processor along with the cooked beetroot. Blitz to a pulp.
Lay 2-3 sheets of clingfilm on top of each other. Cut the salmon side in half. Place one half of the salmon skin side down on the clingfilm. Pour the beetroot and salt mixture over the flesh of the fish and place the other piece of salmon on top, skin side up. Ensure the flesh of the salmon is completely covered in the cure and tightly wrap with clingfilm.
Place the wrapped up salmon into a tray and allow it to rest and chill in the fridge for 48 hours. Turn the fish every 12 hours. After 48 hours the salmon will feel firm to the touch.
Pare the cucumber into thin ribbons along the length, using a potato peeler. Place the ribbons in a bowl, sprinkle with salt and cover with ice cold water. Set aside for an hour to draw out excess water.
After an hour drain thoroughly and wash off any residual salt. Place the ribbons on kitchen paper and dry completely.
Meanwhile place the vinegar, sugar and dill into a saucepan and simmer gently for 5 minutes to dissolve the sugar. Take off the heat and allow to cool slightly.
Place the cucumber ribbons in a plastic container with a tight sealing lid. Pour over the pickling liquor and stir to combine. Allow to cool completely, then cover with lid and place in the fridge for a minimum of two hours but ideally 2 days.
Mix together the horseradish sauce, mustard, vinegar and sugar. Season the mixture with salt and pepper.
Whip the double cream into peaks and stir through the horseradish mixture. Place in the fridge to chill until ready to serve.
Place the avocado and creme fraiche in a bowl and mix together with a stick blender, add the dill and season with salt and further blitz to a smooth cream. Set aside until ready to serve.
After 48 hours remove the salmon from the cling film and discard any excess cure.
Using a sharp knife cut the salmon into thin slices, much as you would if cutting smoked salmon.
Place some of the horseradish sauce on the plate and arrange the sliced salmon on top. Pipe or spoon some avocado cream onto the plate. Arrange the pickled cucumber and cooked beetroot around the plate and garnish with pea shoots and fresh dill fronds. Serve immediately.
Once cut, wrap the salmon tightly in parchment paper and it will keep for 2-3 weeks in the fridge.