For the horseradish sauce, place the horseradish, white wine vinegar and caster sugar into a non-reactive pan and bring to the boil. Remove from the heat, allow to cool, then refrigerate for at least 24 hours.
For the marinade, place the rice wine vinegar, water and sugar into a non-reactive pan and bring to the boil. Reduce the heat and simmer for five minutes, or until syrupy in consistency.
For the beetroot and apple crisps, preheat the oven to 70C/150F/Gas ¼.
Dip the apple and beetroot slices into the marinade and place onto a silicone mat on a baking tray. Transfer into the oven to cook for two hours.
Remove from the oven and allow the crisps to cool.
For the jelly, pour the beetroot juice into a clean pan and bring to the boil. Pour the apple juice into a separate pan and bring to the boil. Skim both the liquids to remove any surface matter, then remove from the heat.
Add one sheet of softened gelatine to each pan of heated juice and stir to dissolve. Strain the beetroot juice through a fine sieve and place into a pouring jug.
Strain the apple juice mixture through a separate, clean fine sieve into a clean jug. Pour each juice mixture into separate small ice cube trays (or very small jelly moulds) and place into the fridge for 12 hours to set.
For the horseradish crème fraîche, place a tablespoon of the horseradish sauce (prepared in step one) and the crème fraîche into a bowl and mix well. Season, to taste, with salt and freshly ground black pepper.
To serve, place two apple crisps and two beetroot crisps onto each of four plates. Place one small slice of smoked eel onto each crisp and top with a small amount of horseradish crème fraîche.
Top with each crisp and eel stack with a jelly of its opposite flavour (apple jelly on beetroot crisp; beetroot jelly on apple crisp). Garnish with rock chives and purple shisho and serve immediately.
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