Pour the condensed milk, vanilla extract, cream and cocoa powder into the bowl of a stand mixer. Whisk using the balloon attachment until you reach the soft peaks stage (will just hold its shape when you lift the whisk).
Whilst the ice cream is being whisked, chop the fudge cake into 1 inch cubes.
Once the ice cream mixture is thick, add in half of the chocolate cake chunks and fold in with a spatula.
Spoon half of the ice cream mixture into a loaf or pie tin (or other freezable container) that has been lined with baking parchment. Sprinkle on half of the remaining chocolate cake chunks. Top with the rest of the ice cream and arrange the remaining chocolate cake chunks on top. Sprinkle on the chocolate curls and place in the freezer for at least 3-4 hours (cover with a lid if freezing for longer).
Take the ice cream out of the freezer approx. 5 minutes before you want to eat it – to allow it to soften slightly.