In a small saucepan, whisk together cream, corn syrup, brown sugar, cocoa powder, salt, and 3 ounces of the chocolate over medium heat. Once the mixture comes to a boil, reduce heat to low.
Simmer, stirring occasionally, for 5 minutes, then remove from heat. Whisk in the remaining 3 ounces chocolate, butter, and peppermint extract until smooth. Allow to cool slightly before serving.
Store in airtight container in refrigerator for up to a week. Warm slightly before serving.