Kahlua Chocolate Pudding

4 ounces semisweet chocolate, chopped
2 tablespoons unsalted butter
2 tablespoons cornstarch
1/4 cup unsweetened cocoa powder
3/4 cup granulated sugar
3 1/2 cups milk
2 large eggs
3 large egg yolks
1/4 cup Kahlua

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 heat.

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 chocolate mixture. 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.