Put 7/8 of the sugar in saucepan with the water. Bring to a boil. Cook until dark in color, about 4 to 5 minutes. Pour immediately into a 4-cup souffle dish. Set aside. Preheat oven to 325 degrees F. Mix coffee, milk, cream, and vanilla into saucepan. Bring to just a boil, stirring frequently. Remove from heat. Set aside. In a bowl, whisk eggs and egg yolks with remaining sugar until creamy. Whisk in hot milk mixture. Place on top of the caramel in the souffle dish. Cover with aluminum foil. Put souffle into a pan and fill the pan with enough water to come half way up sides of the dish. Bake until set, about 40 to 45 minutes.
To turn out, run knife around edge of dish to loosen. Cover with serving plate, hold tightly and invert.