Put the mint leaves in a heavy saucepan with the 1 cup of milk and 1 cup of the cream. Heat until just steaming, don’t let it boil, remove from heat, cover, and let stand for 30-45 minutes. Meanwhile, keep the other 1 cup of cream in the refrigerator.
Strain the milk cream mixture into a separate bowl, pressing against the mint leaves to get the most liquid out of them. Return the milk cream mixture to the saucepan. Add sugar and salt to the mixture. Heat until just steaming again, stirring until sugar has dissolved. Remove from heat.
Whisk the egg yolks in a medium sized bowl. Slowly pour the heated milk cream mixture into the egg yolks, whisking constantly so that the egg yolks are tempered by the warm mixture, but not cooked by it. Scrape the warmed egg yolks back into the saucepan.
Return the saucepan to the stove, stirring the mixture constantly over medium heat with a wooden spoon, scraping the bottom as you stir, until the mixture thickens and coats the spoon. This can take about 10 minutes.
Pour the custard through the strainer (used for the mint leaves) and stir into the cold cream (that has been in the refrigerator) to stop the cooking.
Chill the mixture thoroughly in the refrigerator (at least a couple of hours) or stir the mixture in the bowl placed over the ice bath until thoroughly chilled (20 minutes or so).
Once the ice cream has been made in the ice cream maker it should be pretty soft. Gently fold in the finely chopped chocolate. Put in an airtight container and place in the freezer for at least an hour, preferably several hours. If it has been frozen for more than a day, you may need to let it sit at room temperature for a few minutes to soften it before serving.