Frozen profiteroles with Neapolitan ice cream

Method

1. For the choux buns, put the butter and 150ml water in a saucepan set over a medium heat. When the butter has melted, turn up the heat and bring to a rolling boil.
2. Meanwhile, in a mixing bowl, combine the flour, sugar and salt then, in one go, tip into the boiling butter/water mixture. Beat strongly with a wooden spoon until the mix clumps into a ball that fully comes away from the sides of the pan. Tip the mixture into a bowl and use the spoon to spread it up the sides (to help it cool quickly). Leave to cool to room temperature.
3. Heat the oven to 220°C/200°C fan/gas 7. Once the mixture has cooled, beat in the 4 eggs, little by little, only adding more once the previous addition is fully mixed in. The mix will look as though it’s about to split but it will come back together after beating. You may not need all the eggs or you might have to add an extra splash of milk to get the right dropping consistency (it should drop slowly off the spoon in a clump).
4. Transfer the choux mixture to the piping bag, then pipe 12 buns, each about 5cm wide and 3cm deep, onto each of the prepared baking sheets, spaced at least 3cm apart (24 buns in total). Use your finger to brush a little beaten egg over each one to glaze and smooth out any peaks. Bake for 20 minutes, then use a skewer to poke a small hole in the bottom of each one to let out the steam. With the hole on top, bake for 2-3 minutes more until golden and crisp. Cool on a wire rack (see Make Ahead).
5. Slice each profiterole in half horizontally. Fill a third of the profiteroles with chocolate ice cream, a third with strawberry and a third with vanilla, then reassemble. Transfer the profiteroles to baking sheets and freeze for 1 hour or until the ice cream is firm (see Make Ahead).
6. When you’re ready to serve, make the caramel (see tip). Put the sugar in a small saucepan with 3 tablespoons water over a medium heat and cook, swirling the pan regularly, for 6-8 minutes until you get a dark golden caramel. Remove from the heat and cool slightly. Carefully spoon caramel over the tops of the profiteroles, then crumble over freeze-dried raspberries (see Make Ahead). Arrange the profiteroles in a circle on a platter and serve immediately.