Preiheat oven to 350 degrees. Place sugar and water in a round cake pan. Heat in stove top over low heat, without stirring, until sugar melts and syrup is golden brown. Remove from heat and set aside.
In a medium saucepan add the milk, heavy cream, coffee and sugar. Mix well with a whisk and cook over low heat, until barely warm. Then add the egg and egg white, stirring constantly. As soon everything is well combined and just warmed through, remove from heat**don't over heat or boil**.
Pour over prepared caramel. Place this pan inside a larger one. Fill larger pan half-way with very hot water. Cover everything with foil paper and bake 50-60 minutes or until set (lift foil to check). Remove from oven and water bath and place in a rack too cool. When it is at room temperature, unmold into a serving plate. Serve at room temperature or place in refrigerator for up to 1 day, tightly covered.