Line a baking sheet with parchment paper or a silicone baking mat, then break each graham cracker sheet in half and position the graham cracker squares to cover the bottom of the baking sheet.
Pour the white chocolate chips into a microwave safe bowl and microwave in 30 second intervals, stirring in between, until melted and smooth.
In a medium mixing bowl, combine softened butter and the melted white chocolate, mix until smooth, then add in the heavy whipping cream, peppermint extract, and green food coloring, mix again to combine.
Pour in the powdered sugar, then mix again until smooth. Evenly spread the peppermint filling over the graham crackers, then set aside.
In another microwave safe bowl, combine semi-sweet chocolate chips with vegetable oil, then microwave in 30 second intervals, stirring in between, until melted and smooth.
Evenly spread the melted chocolate over the peppermint layer, then sprinkle with chopped Andes Mints.
Transfer to the fridge for at least 30 minutes to set the chocolate before cutting or breaking the bark into pieces.