In a pot over medium high heat, add the cream, milk, mint leaves cream and stout. Bring to a gentle simmer. Remove from heat, remove and discard mint leaves, and stir in the chocolate until melted.

In a separate bowl, add the egg yolks and the sugar, whisk until well combined. Slowly add the chocolate milk, whisking continually, until about 1/2 the mixture has been added to the egg yolks. Add the egg yolk mixture back into pot, whisk until well combined. Return pot to heat and bring to a mild simmer.

Refrigerator until chilled, about 3 hours.

Churn in ice cream maker according to manufactures directions. Chill until firm.