In a large bowl, beat the egg yolks lightly with a whisk, about 30 seconds. Add the cocoa, sugar, and 2 tablespoons of the milk and beat until thickened and dark, glossy brown in color, about 3 minutes.
In a small saucepan, heat 1 1/2 cups half-and-half and the cream over medium-low heat until a candy thermometer registers150 degrees F. (You may see steam rising from the pan, but the milk and cream should not start to boil.)
With a sharp knife, slice the vanilla bean lengthwise, scrape the tiny black seeds into the half-and-half, and add the vanilla bean to the pan. Add the grits and continue to cook, stirring occasionally and maintaining the temperature around 150 degrees F, until the grits swell and the mixture thickens to the consistency of a thin porridge, about 10 to 20 minutes, depending on the freshness of the grits and the coarseness of the grind. Remove the vanilla bean and discard.
Whisk 1 cup of the half-and-half and grits mixture slowly into the cocoa mixture, stirring constantly until the liquids are thoroughly incorporated. Add the chopped chocolate to the grits mixture remaining in the saucepan and stir until it dissolves, 2 to 3 minutes. Stir the cocoa mixture into the grits and chocolate mixture and cook over low heat, stirring occasionally to prevent scorching, until the custard thickens to the texture of a thick, liquid pudding, 8 to 12 minutes. Let cool to room temperature and transfer to a container. Press plastic wrap onto the surface of the custard and refrigerate for 4 hours or overnight, until the custard is very cold.
Pour the custard into an ice cream maker and churn according to the manufacturer's instructions until the ice cream becomes very thick and holds its shape. Quickly transfer the ice cream to a container with a tight-fitting lid. If there is any space between the surface of the ice cream and the lid, pat a sheet of plastic wrap on the surface. Cover the container.
Freeze the ice cream until it has hardened, at least 2 hours. Remove from the freezer 10 minutes before serving and remove the plastic wrap.
Serve small scoops of ice cream in bowls, and garnish with shaved chocolate or for fun, a pinch of dry, raw grits.