Pour the milk into a saucepan and add the sugar. Bring to a boil, stirring, until the sugar has dissolved. Remove from the heat and stir in the chocolate. continue to stir until all of the chocolate is melted.

Pour the egg yolks into a heatproof bowl and beat for 5 minutes, or until the beaters leave a faint trail when lifted from the mixture. Whisk some of the warm chocolate mixture into the egg yolks (about ¼ cup), then gradually beat in the rest of the hot milk.

Place the bowl over a saucepan of gently boiling water. Stir continuously for about 10 minutes, until the mixture reaches a temperature of 185F, or is thick enough to coat the back of a spoon. Be careful not to let it boil.

Strain the mixture through a fine strainer into a bowl. Stir in the vanilla extract. Set the bottom of the pitcher in iced water until cold, then cover with plastic wrap and chill for 2 hours or up to overnight.

Meanwhile, pour the stout into a saucepan and bring to a boil. Reduce the heat and simmer briskly for 8 minutes, or until reduced to 1 cup. Pour into a jar, let cool, cover with a lid, and then chill in the refrigerator with the custard.

Stir the cream and chilled stout into the chocolate mixture, mixing well. Pour the mixture into the bowl of an ice cream machine. Churn and freeze following the manufacturer’s instructions. Alternatively, if you don’t have an ice cream machine, pour the mixture into a shallow freezer-proof container, cover with plastic wrap, and freeze for about 2 hours, until it begins to harden around the edges. Beat the partially frozen ice cream by hand until smooth to get rid of any ice crystals that have formed. Freeze again, repeat the process twice, then freeze until completely firm.

Serve in chilled dishes, sprinkled with grated chocolate.