In a heavy saucepan, heat cream, stout, milk, and honey until bubbly. In a medium bowl, beat egg yolks and sugar with an electric mixer on medium to high speed until fluffy. Beat in the cocoa powder until well combined. Gradually stir hot stout mixture into egg mixture until just combined. Return to saucepan. Cook and stir over medium heat until slightly thickened and just begins to bubble around edges (don't overcook).
In a large bowl, place semisweet chocolate pieces. Pour hot egg mixture over chocolate pieces. Stir with a wire whisk until the chocolate is melted. Cool; cover and chill thoroughly.
Pour the chocolate mixture into a 2-quart ice cream container. Freeze according to manufacturer's directions. Makes 1 quart (8 servings).