Melt both the chocolates in separate saucepans or bowls if melting the microwave and set aside to cool slightly.
Ice Cream;
Line a 9"x5" loaf pan with cling film and set aside.
*In a large mixing bowl and a beater or stand mixer, beat the cream until soft peaks form.
Add the condensed milk and the vanilla extract and lightly beat until it is all combined.
Divide the mixture into three separate bowls, trying to keep the amounts of each even.
While stirring with a spoon, pour in the melted dark chocolate to one of the bowls and fold it through the ice cream mixture.
Pour this into the base of the load pan and spread out in an even layer and place in the freezer for 20 minutes.
While stirring with a spoon, pour in the melted milk chocolate to one of the bowls and fold it through the ice cream mixture.
Place both this and the vanilla ice cream bowl into the fridge while the dark chocolate layer is freezing.
Once the dark chocolate layer is set enough, Layer over half of the Oreos and then pour over the milk chocolate ice cream and place back in the freezer for a further 20 minutes or so.
Repeat with the remaining Oreos and vanilla layer. Freeze until set. I like to leave it for at least 8 hours but depending on your freezer, it could take less time.
When ready to serve, heat the cream until boiling point and then pour over the dark chocolate buttons, stirring until smooth and glossy.
Drizzle the ganache over the layer ice cream cake and then slice.
Notes
Alternatively, you can use store bought ice cream to layer.*You can make the ice cream in two batches if needed.