Melt chocolate and butter in the top of a double boiler over barely simmering
water or in a small bowl set over a saucepan of just-simmering water. Remove from
In a medium-size bowl, whisk cornstarch, cocoa and 1/4 cup of the sugar into
1/2 cup of the milk.
In a medium-size heavy-bottom saucepan, combine remaining 3 cups milk and 1/2
cup sugar and bring just to a scald over medium heat. Whisk the hot liquid into
the cornstarch mixture, then return the mixture to the saucepan and cook, whisking
constantly and scraping the bottom of the pan, until tiny bubbles boil up for 10
seconds. Remove from the heat.
Put the eggs and egg yolks into the medium bowl. Whisking gently, but constantly,
slowly drizzle 1 cup of the hot liquid into them. Return everything to the saucepan
and cook, whisking constantly and scraping the bottom of the pan, until tiny bubbles
boil up for 3 seconds. Remove from the heat and stir in the Kahlua.
Strain pudding through a fine sieve into a bowl. Thoroughly stir in the melted
Divide pudding among 8 serving bowls. Place a piece of wax paper
directly on the surface of each one to prevent a skin from forming.
Let cool for 2 to 3 hours, then refrigerate until chilled.