In a medium saucepan, heat the cream, milk, sugar and salt over medium heat; whisking to dissolve the sugar (about 4 to 5 minutes).
In a separate bowl, whisk the egg yolks.
Gradually pour about 1 cup of the hot milk mixture into the egg yolk bowl, while continually whisking to temper the eggs.
Add the tempered egg yolk mixture back to the pan while whisking until it just comes to a simmer.
Remove the pan from the heat, then add the mint and vanilla extract.
Pour the ice cream base through a fine mesh strainer and chill completely either over an ice bath or in the refrigerator.
Spin the mint ice cream base in a maker according to the manufacturer's instructions.
While the ice cream spins, melt the chocolate in a double boiler.
In a chilled container where you will store the ice cream, drizzle chocolate over the bottom.
When the ice cream is finished spinning, add a layer of ice cream to the container, then another drizzle of chocolate. Continue this process until all of the ice cream is in the container, then freeze for at least 5 hours, or overnight before serving.