Line a sheet tray or roasting pan with parchment paper or a silicone baking mat. Fill a small saucepan with about 2 inches of water and bring it to a gentle simmer over medium heat. Set a large heatproof metal or glass bowl over the saucepan, making sure the bowl is completely dry and the water does not touch the bottom. Even a small amount of moisture can cause the chocolate to seize.
Add the chopped dark chocolate to the bowl and reduce the heat to low. Stir gently with a rubber spatula until the chocolate is fully melted and smooth, then remove the bowl from the heat. Transfer the white chocolate to a separate heatproof bowl and repeat the same process to melt it.
Alternate spooning the dark and white chocolate onto the prepared baking sheet, creating a swirled pattern about ½ inch thick. Sprinkle the chopped peppermint evenly over the melted chocolate. Let the bark set at room temperature until it begins to firm up.
Once solid, cover the chocolate with parchment paper and transfer the tray to the refrigerator for a few hours or overnight to fully harden. Break the bark into pieces using a sharp knife, then store in an airtight container in the refrigerator for up to one week.