In a medium, heavy saucepan, combine the chopped mint leaves, heavy cream and milk and, stirring constantly, bring to a simmer. Remove from the heat and let steep, stirring occasionally, for 1 hour.
Using a fine sieve, strain the cream mixture into a medium bowl, pressing with a wooden spoon to extract as much liquid as possible. Add the liquid to the saucepan, stir in the chocolate, sugar and salt, and cook over low heat, stirring frequently, until the chocolate is melted. Let cool, then transfer the mixture to a bowl and refrigerate for at least 1 hour.
Scrape the chilled mint-chocolate mixture into an ice cream maker and freeze according to the manufacturer's instructions. Garnish with the mint sprigs before serving.