Dissolve the cornstarch in 50ml whole milk, leave to rest.
Toss the milk and the basil leaves into the blender and whizz on high.
In a small saucepan combine the basil milk mixture, the heavy cream, sugar and salt, simmer just until boiling, take off heat, cover and leave to steep for 10min. Run the mixture through a very fine sieve, return it to the saucepan and heat again. Stir the cornstarch milk mixture into the saucepan and cook on medium stirring constantly until thickened. Remove from heat, cool to room temperature, transfer into a clean jug, put it into the refrigerator and cool overnight.
Freeze the ice cream in your ice cream maker according to the manufacturer's instructions and store in an airtight container in the freezer for at least 4 hours until set or spoon right away.