Combine cream, milk, and sugar in a saucepan over medium heat. Stir until sugar has dissolved, about 5 minutes.
Split the vanilla bean lengthwise with a sharp knife and scrape seeds into cream mixture. Place bean pod into mixture and bring to a boil. Remove from heat and discard vanilla bean pod.
Place egg yolks in a bowl. Gradually whisk in 1 cup hot cream mixture.
Whisk the egg yolk mixture back into the saucepan and place over medium heat. Whisk constantly until slightly thickened, about 2 to 3 minutes. Mixture should coat the back of a spoon. Do not let the mixture boil.
Transfer cream mixture to a bowl and chill until cold, at least 2 hours to overnight.
Simmer Irish stout beer in a saucepan over low heat until reduced to 2/3 cup, about 15 minutes. Chill the stout beer syrup at least 2 hours to overnight.
Whisk together chilled cream mixture and beer syrup; pour into an ice cream maker and freeze according to manufacturer’s directions.
When machine has finished, pack ice cream into a airtight container and store in freezer.
1 teaspoon vanilla extract may be substituted for the vanilla bean.
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