1. In a medium saucepan, warm the milk, sugar, 1 cup (250 ml) heavy cream, salt, and mint.
2. Once the mixture is hot and steaming, remove from heat, cover, and let stand for an hour to infuse the mint flavor.
3. Remove the mint with a strainer, then press down with a spatula firmly to extract as much mint flavor and color as possible. (You can also use well-washed hands to do it as well, making sure the mixture isn’t too hot to safely handle.) Once the flavor is squeezed out, discard the mint.
4. Pour the remaining heavy cream into a large bowl and set the strainer over the top.
5. Rewarm the infused milk. In a separate bowl, whisk together the egg yolks, then slowly pour some of the warm mint mixture into the yolks, whisking constantly, then scrape the warmed yolks back into the saucepan.
6. Cook the custard, stirring constantly with a heatproof spatula, until the mixture thickens and coats the spatula. If using an instant read thermometer, it should read around 170ºF (77ºC).
7. Immediately strain the mixture into the cream, then stir the mixture over an ice bath until cool.
8. Refrigerate the mixture thoroughly, preferably overnight, then freeze it in your ice cream maker according to the manufacturer’s instructions.
While the mixture is freezing, melt the chocolate in a small bowl over a pot of simmering water, or in a microwave oven on low power, stirring until smooth. Place a storage container in the freezer.
9. When the ice cream in the machine is ready, scribble some of the chocolate into the container, then add a layer of the just-churned ice cream to the container. Scribble melted chocolate over the top of the ice cream, then quickly stir it in, breaking up the chocolate into irregular pieces. Continue layering the ice cream, scribbling more chocolate and stirring as you go.
When finished, cover and freeze until firm.