Sift together the cocoa and cornstarch in a small bowl. Add 1 tablespoon water and stir until smooth.
Combine the milk, sugar and chocolate chips in a 4-cup glass measuring cup. Microwave at 100 percent, until the chocolate melts completely, stopping to stir twice, about 3 minutes. Whisk in the cocoa-cornstarch mixture. Then whisk in egg and yolks. Microwave for 2 minutes, stir well and the microwave for another 2 minutes. Scrape the mixture into a food processor and add the butter and vanilla. Process until smooth. Pour into 4 individual cups and chill.