Dissolve the cornstarch in 50ml whole milk, leave to rest.
In a small saucepan over medium heat combine the heavy cream, the leftover whole milk, sugar, pinch of salt, bring to an almost boil, add matcha powder, whisk until dissolved, add the cornstarch milk and cook constantly stirring until thickened. Take off heat, add the cream cheese, whisk until combined. Cool to room temperature, then transfer into the fridge overnight.
Freeze in your ice cream maker according to the manufacturer's instructions adding the chopped green tea KitKat candy at the last couple of minutes of churning. Store in an airtight container or spoon right away.