Twist the Oreo sandwiches apart. Scrape the cream off.
Break the chocolate biscuits by hand into small, chunky pieces. Avoid turning them into fine crumbs; you want texture!
In a medium bowl, whip the softened butter until it is light, fluffy, and pale in color.
Melt 113g of white chocolate using a double boiler (a bowl over a pot of simmering water) or microwave(on high, stir every 15 seconds until smooth). Let the white chocolate cool to room temperature before using it.
Let the chocolate cool to room temperature (it should still be liquid but not warm to the touch). Fold the chocolate into the whipped butter until smooth.
Add the Oreo pieces and mix until every biscuit chunk is coated.
Line a baking pan with parchment paper. Add the mixture in three additions.
Use a flat-bottomed glass or a meat presser to firmly pack down each layer. This prevents the cake from crumbling when sliced.
Refrigerate for at least 4 hours until completely firm.
Remove the chilled cake from the pan and peel off the parchment. Place the cake on a wire cooling rack with a clean baking tray underneath to catch drips.
Melt additional 227g white chocolate. Pour it slowly over the center of the cake, use a offset spatula to gently guide it over the edges and sides.
If there are bare spots, scrape the chocolate from the tray below, re-melt it if necessary, and apply a second coat.
Return the cake to the fridge for 20 minutes to let the coating set.
Slice it up and dig in!