Twist the oreos to separate them (see notes), and scrape off the cream filling (either discard the filling...or eat it, if you're into that.)
Place 2/3 of the chocolate into a heatproof bowl set over a pan of simmering water. Stir occasionally until almost fully melted then remove the bowl from the pan. Stir in the remaining 1/3 of finely chopped chocolate, mixing until full melted, then stir in the peppermint oil well.
Dip an oreo half in the melted chocolate, turn to coat using a fork. Use the fork to remove the oreo from the chocolate, tap it on the edge of the bowl a few times (to let excess chocolate drip off).
Transfer to a baking tray lined with baking paper. Repeat with all the oreo halves.
Leave at room temperature until set.
Store in an airtight container somewhere cool and out of direct sunlight for up to 2 weeks.