Add cream of tartar to egg whites. Mixing smoothly with a whisk, gradually add milk. Stir until the chocolate is completely melted and smooth. Whisk in whole egg and yolk mixture. Beat egg whites with cream of tartar at medium speed until whites hold soft peaks.
Scrape batter into prepared cake pan, and smooth the top.
Set cake pan in another pan that is at least 2 inches wider and 2 inches deep. Set pans in oven. Lift cake pan from water, and set on a rack to cool. When cake is cool to the touch, cover it with plastic wrap, and chill until thoroughly cold, at least 8 hours or up to 2 days. To release cake, slide a thin knife between rim and cake.