Preheat the oven to 180C/160C Fan/Gas 4.
Put the coconut chips in a dry frying pan and toast them until golden-brown, stirring regularly. Toast the pistachios and fennel seeds in the same way, then transfer the pistachios and fennel seeds to a food processor and pulse until they are just broken. Set aside to cool.
In a large bowl, cream together butter and sugar until pale and fluffy. Mix in the eggs and coconut essence.
Combine the flour, baking powder, salt, toasted coconut, pistachios and three-quarters of the fennel seeds. Add to the butter mixture and mix until well combined (the mixture will be quite stiff so you will find it easier to use an electric mixer). Divide the dough into 2 equal mounds.
Line 2 baking trays with baking parchment. Place a mound of dough onto each tray and shape them into a rectangle approximately 25x8cm/10x3¼in. Bake for 35 minutes.
Remove the dough from the oven and set aside to cool on the tray for 15 minutes. Reduce the oven temperature to 160C/140C Fan/Gas 2.
Slice each log into pieces about 1cm/½in thick. Each log should produce about 12 biscotti.
Place the pieces cut-side down on the baking trays and return them to the oven. Bake for 10 minutes on each side, or until they are golden-brown and crisp. Leave to cool on a wire rack.
For the coconut brittle, line a baking tray with non-stick baking paper.
Add the sugar, butter and 125ml/4½oz water to a large saucepan. Heat gently until the sugar dissolves. Using a sugar thermometer, continue to heat the mixture to 160C, or until a caramel forms. Remove from the heat immediately and stir in the coconut. Stir in the bicarbonate of soda – the caramel will start to foam so take care not to burn yourself, melted sugar is very hot. Pour onto the prepared tray and leave to cool.
When cool, break the brittle into large pieces and add to a food processor. Add the reserved fennel seeds and pulse until broken into a coarse powder. Transfer to a shallow dish.
Melt the dark chocolate in a heatproof bowl over a pan of simmering water. Dip the long side of the biscotti in the melted chocolate and then into the coconut brittle. Set aside until the chocolate is set, then serve.