Bring on the night by melting the semisweet chocolate in the top half of a double boiler over medium heat. Stir the chocolate constantly with a rubber spatula until it is completely melted and smooth, then remove from the heat and set aside. Heat the half-and-half, 1/4 cup sugar, and the cocoa in a 3-quart saucepan over medium-high heat. When hot, whisk to dissolve the sugar. Bring to a boil. While the cream is heating, whisk the egg yolks, remaining sugar and cornstarch in a medium bowl until slightly thickened and lemon-colored. Pour the boiling half-and-half mixture slowly into the egg yolks and stir to combine. Return the mixture to the saucepan and heat over medium-high heat, stirring constantly, until it begins to boil and becomes quite thick, about 30 seconds. Remove the pan from the heat and transfer the mixture to a large bowl. Add the melted chocolate, then place the bowl in ice water and stir the pudding until it is cold. Fold all but 2 tablespoons of chopped white chocolate into the pudding. Portion 3/4 cup of the pudding into each of 4 dessert dishes and sprinkle 1/2 tablespoon of the remaining white chocolate over the top of each.