To make the chocolate biscuits, use an electric mixer to beat butter and sugar in a bowl until pale and creamy. Add the egg and beat until combined. Sift in cocoa and combined flour and stir to combine. Turn onto floured surface and shape into a ball. Divide dough in half. Wrap each portion in plastic wrap and place in the fridge for 30 mins to chill.
Roll each dough portion between 2 sheets of non-stick baking paper to 5mm-thick discs. Place in the fridge for 10-15 mins or until firm.
Preheat oven to 180°C. Line two baking trays with non-stick baking paper. Use a 7cm round cutter to cut discs from the dough. Place on trays about 2cm apart to allow room for spreading. Bake for 12 mins or until firm to touch. Set aside on trays to cool completely.
Meanwhile, to make the raspberry ice-cream, combine the cream and milk in a saucepan over medium heat. Bring to a simmer. Use an electric mixer to whisk the egg yolks and sugar until very pale and thick. Gradually add the hot cream mixture in a thin, steady stream, lightly whisking continually. Transfer the mixture to a clean saucepan and place over medium-low heat. Cook, stirring with a wooden spoon, for 10 mins or until custard thickens slightly and coats the back of the spoon (be careful not to overcook as the custard may curdle). Set aside to cool.
Place the raspberries in a saucepan over medium heat. Cook, stirring, for 5 mins or until the raspberries soften and begin to release their juices. Strain through a fine sieve into a bowl, using the back of a spatula to push as much pulp through as possible. Stir into the custard mixture. Add enough red food colouring to turn the mixture a medium pink. Pour the mixture into a metal 20cm x 30cm lamington pan. Cover with foil. Place in freezer for 6 hours or until set. Use a metal spoon to break up the ice-cream. Place in a bowl. Use an electric mixer to beat until smooth and pale.
Line the clean lamington pan with a large sheet of baking paper, allowing the sides to overhang. Return ice-cream to the lined pan. Cover with foil and place in freezer for 4 hours or until firm.
Turn the ice-cream onto a clean work surface. Use a 7cm round pastry cutter to cut discs from the ice-cream. Working quickly, place 1 ice-cream disc between 2 biscuits. Repeat with the remaining ice-cream and biscuits. Serve immediately or return ice-cream sandwiches to the freezer.