In small, heavy bottomed saucepan, combine milk, cream, and sugar. Warm over low heat, stirring often, just to simmer. Quickly stir in coffee to dissolve. Remove from heat. Very gradually add remaining hot liquid, whisking until smooth after each addition.
Scrape bowl occasionally with rubber spatula.
If necessary, return to pot and reheat over low heat, stirring often, until very hot. Stir in vanilla. Serve at once. Makes 2 to 3 servings.