The secret to David Burke's baked Alaska recipe is a little Kahlúa in the ice cream.
Bring the milk, heavy cream, cocoa powder, and 12 ounces of sugar to a boil. Slowly add in the yolks and the rest of the sugar to the boiling liquid. Next add the chocolate, the Kahlúa and the vanilla extract. Mix together until nappe, or thick enough to coat the back of a spoon. Let cool. Then fill the chocolate mix into dome molds and freeze.
In a mixer on medium speed, mix together the first 3 ingredients until firm. Add the confectioner's sugar and mix on high until firm and shiny.
Preheat the oven to 350 degrees.
Combine all of the ingredients, except the chocolate, into a stand mixer and beat for 30 seconds. Add the chocolate and beat for 3 minutes on high. Pour the batter into a 9-inch greased cake pan and bake for 45 minutes.
To assemble the Alaska:
After cake has cooled, cut out small round pieces. Place one piece of cake inside each Alaska dome with the ice cream. Top with a dallop of meringue. Bake for 2 minutes on low heat to brown meringue. Serve!