Preheat the oven to 180'C / Fan 160'C / Gas Mark 4. Fill a 12-hole baking tin with cupcake cases. Set aside while you make the cake batter.
Add the butter, sugar and vanilla extract to a large mixing bowl and beat with an electric whisk until pale and creamy. (TIP: If the butter is hard, zap it in the microwave for 10-15 seconds before adding it to the mixing bowl to make it easier!)
Crack the eggs into the mixing bowl and beat again for 30 seconds to combine. Scrape down the sides of the bowl using a spatula.
Sift in the self-raising gluten free flour, cocoa powder and xantham gum, then add the milk and beat together with the electric whisk until everything is fully combined. You want a fairly thick batter which looks light and fluffy.
Place a gluten free Oreo at the bottom of each cupcake case, and then spoon the mixture evenly between the cases on top of the cookies. Place in the centre of an oven and bake for 20-22 minutes. The cupcakes are done when they are well-risen and a skewer inserted in the middle comes out clean.
Once cooked, remove from the oven and place on a cooling rack. Cool in the tray for 10 minutes before removing the cakes from the tray to cool completely.
To make the frosting:
Blitz the gluten free Oreos (biscuit and filling) in a food processor until they form a fine crumb.
Add the butter, icing sugar and milk to a large mixing bowl and beat with an electric whisk on a low speed until it becomes a smooth, fluffy buttercream. Add the crushed gluten free Oreos and mix until fully combined.
Spoon the mixture into a piping bag (see notes) and, once the cupcakes are completely cool, decorate them with a swirl of buttercream. I used a 1M piping tip which has a slightly more open nozzle - just in case there are any larger chunks of Oreos!
Decorate with extra gluten free Oreos - I popped half an Oreo in each cupcake - alternatively you could break them up and crumble them on top too or place a whole Oreo on top of each (see notes if making in advance).
Notes
For the frosting, it's important to use room temperature butter to get the right consistency. If it becomes very soft once beaten (especially likely on a hot day) then place the buttercream in the piping bag and refrigerate for 15-20 minutes until it's an easy consistency to pipe.
These cupcakes will keep for a couple of days - however the Oreos may go a little soft after a day or so. If making in advance, I'd recommend not topping with the decorative Oreos until just before serving.