Preheat the oven to 200ºC/400ºF/gas 6 and grease a baking sheet.
For the choux pastry, melt the butter in a saucepan with 220ml of water then bring to a rolling boil.
Sift the flour and 1 pinch of fine sea salt onto a piece of folded greaseproof paper, then quickly pour into the boiling water.
Beat the pastry mixture vigorously with a wooden spoon until it’s smooth and the bottom of the pan is beginning to fur, then spread out on a plate and leave to cool for 20 minutes.
Meanwhile, prepare the filling. Crush the pistachios. Place the cream and most of the pistachios in a small saucepan and slowly bring to the boil. Remove from the heat and leave to infuse until ready to use.
Beat the eggs. Once the pastry is cool, return it to the saucepan and gradually beat in the beaten egg until the pastry mixture reaches a consistency that lazily drops off the spoon (you may not need all of the beaten egg).
Using teaspoons, space out small dollops of pastry mixture on the prepared baking sheet. Bake for 25 minutes, or until golden brown.
Once cooked, use a skewer or drinking straw to pierce holes in the bases of the profiteroles, then leave them upside down on a wire rack to dry completely.
When you’re ready to fill the profiteroles, strain the cream and discard the pistachios. Whip the cream with the icing sugar and vanilla essence until it holds its shape. Transfer to a piping bag and pipe a teaspoonful or so into the centre of each profiterole.
Break the chocolate into bites, then melt in a heatproof bowl set over a pan of simmering water (without letting the bowl touch the water).
Arrange the profiteroles on a platter and drizzle over some of the melted chocolate. Serve the leftover chocolate in a small jug on the side.