Place the egg yolks in a mixing bowl with the sugar and whisk until pale and fluffy. Sprinkle the cornflour over the top and whisk in.
Heat the milk in a saucepan until just beginning to bubble around the edge of the pan. Slowly stir the hot milk into the egg mixture. Return the mixture to the pan.
Add the chopped basil and cook gently stirring constantly until the mixture thickens very slightly.
Pour the mixture back into the mixing bowl and allow to cool. When completely cold, cover and chill for at least 4 hours or over night.
Strain the mixture though a fine sieve, pressing the basil firmly with a spoon.
Pour the cream into the cold mixture and whisk in. Pour into an ice cream maker and following the manufacturers instructions, churn until frozen. If you don't have an ice cream maker pour into a shallow container and freeze for about 2 hours until beginning to firm. Whizz in a food processor or beat with an electric whisk to break up the forming ice crystals. Return to the freezer for another couple of hours and repeat the freezing and beating 2 or 3 more times until you have a smooth iced mixture, then transfer to a suitable container cover and freeze until firm.
To serve, move from the freezer to the refrigerator about 20 minutes before serving.