Melt the white chocolate chips. While this is cooling down, make the filling. Stir it occasionally to prevent the edges from getting hard.
Put the butter, powdered sugar, heavy cream, peppermint, and vanilla in a bowl of a stand mixer, fitted with the paddle attachment, and whip until it's all combined and fluffy.
By now, the white chocolate should be cooled but not hard. Turn the mixer on medium and slowly add the white chocolate then turn it up to high and whip until combined.
Add the Oreos and mix until combined