For the coffee panna cotta, chill a large jug or bowl in the freezer.
Heat the double cream, vanilla pod and seeds and sugar in a saucepan until just boiling. Remove the pan from heat, add the soaked gelatine and buttermilk and whisk until well combined.
Pass the mixture through a fine sieve into the chilled jug, and then stir in the coffee.
Return the jug to the fridge and whisk the mixture every five minutes until it begins to set.
Pour the mixture into dariole moulds or ramekins, and chill in the fridge for at least two hours, or until completely set.
For the doughnuts, warm the milk gently in a saucepan. Mix the flour, sugar, salt and yeast in a free-standing mixer. Add the warm milk and egg and mix to a sticky dough. Using a paddle attachment, knead for about 5 minutes until smooth and elastic.
With the mixer running, gradually add the softened butter a little at a time kneading in between each addition. This will take about 10 minutes.
Flour a work surface and turn out the dough. Continue to knead until smooth, shiny and no longer sticky. Place the dough in a large bowl, cover and leave in a warm place to rise for 2 hours, or until doubled in size. Mould the dough into small balls and place on a lined baking tray and leave to rise again for 20 minutes.
Heat the oil in a deep fat fryer or a deep-sided, heavy bottomed pan to 190C, or until a breadcrumb sizzles and turns golden-brown when dropped into it. (Caution: Hot oil can be dangerous. Do not leave unattended.)
Carefully lower the doughnuts into the fat and fry for 3-4 minutes until golden-brown. Drain on kitchen paper. Transfer to a plate and dust with caster sugar.
For the chocolate sauce, melt the chocolate in a bowl set over a pan of simmering water (make sure the bottom of the bowl does not touch the water).
Heat the sugar in a pan with 100ml/3½fl oz water, stirring until the sugar dissolves. Bring to the boil.
Stir the sugar syrup into the melted chocolate until smooth and shiny.
To serve, place the base of the dariole moulds in boiling water to loosen the panna cotta. Place on a serving plate alongside the doughnuts and chocolate sauce. Garnish with the crushed nuts and mint.