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Preheat the oven to 200ºC. Place water, cubed butter and salt in the food processor fitted with the kneading/grinding tool. Set the food processor at speed 3 at 90°C for 8 mins. At the end of the program, add the flour and mix at speed 6 for 2 mins.
Place the mixture in a separate bowl and wash the food processor bowl. Return the pastry to the food processor fitted with the kneading/grinding tool. Mix at speed 6 adding the eggs one by one to obtain a thick shiny paste (but you may not need all of the last egg). Leave running for 2 mins.
Use a piping bag, place small heaps of the mixture onto a baking tray covered with baking paper. Bake for 20 to 25 mins without opening the oven door or until risen and a deep golden brown. Place the chopped chocolate and cream in the cleaned food processor bowl fitted with the kneading/grinding tool and melt at 60°C at speed 4 for 5 mins.
Scrape down the sides then mix at speed 7 for 1 min. Meanwhile, gently make slits in the cooked choux buns and fill with the vanilla ice cream. Serve immediately with the hot chocolate sauce.