In a medium heatproof bowl, combine the 3 ounces of chopped chocolate with the butter. Sift the cornstarch and cocoa powder into a medium saucepan. Whisk in the granulated sugar and 1 1/2 teaspoons of the tea. Whisk in the milk. Bring to a boil over moderate heat and cook, whisking constantly, until very thick, about 2 minutes. Strain through a fine sieve over the chocolate. Let stand for 30 seconds, then whisk until smooth. Spoon the mixture into six 1-cup ramekins. Press plastic wrap directly on the surface of the puddings and let cool, then refrigerate until chilled, at least 1 hour.