In a heavy bottomed saucepan, combine the half & half, heavy cream, sugar, cocoa powder and salt. Whisk until the cocoa powder is mixed in.
Heat over low or medium-low heat for 10 minutes, stirring occasionally, until the sugar is dissolved.
Pour into a bowl, stir in the peppermint extract, and chill in the fridge for at least 2 hours, or until cold.
Churn the mixture in an ice cream maker, according to the manufacturer’s directions (mine churned 35 minutes); during the last 2 minutes, add in the Thin Mint crumbles. Scrape into a container, cover, and freeze until firm (a few hours).