Line a rimmed baking sheet with parchment; set aside.
Crush the peppermint candies into small bits; separate out the fine dust.
Melt dark chocolate with 1 tsp oil in a bowl over gentle heat, stirring until silky.
Spread dark chocolate evenly on the parchment, about 1/4-inch thick. Chill 10 minutes to set lightly.
Melt white chocolate with remaining oil until smooth. Stir in peppermint extract and salt.
Fold a small handful of crushed peppermint into the white chocolate.
Pour white chocolate over the set dark layer and spread gently. Sprinkle remaining peppermint on top.
Press lightly so pieces adhere. Chill until firm, 30–45 minutes. Break into shards and serve.