"The rich chocolaty deliciousness of hot chocolate, refreshingly frozen. My son and his friends cheer when I make this decadent treat! Top each serving with whipped cream. Sprinkle additional chocolate chips or chocolate shavings, if desired. Serve with a straw or spoon."
Place semisweet chocolate chips, milk chocolate chips, sugar, hot chocolate mix, and butter into the top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate chips start to melt, about 5 minutes.
Stir evaporated milk slowly into the chocolate mixture until chocolate chips are halfway melted, about 3 minutes. Remove from heat; continue stirring sauce is until smooth and velvety, about 2 minutes more. Mix in vanilla extract. Let sauce cool to room temperature, at least 20 minutes.
Place 1 cup chocolate sauce, 4 cups ice, and 1 cup milk in a blender. Cover and blend until smooth; pour into 2 individual glasses. Refrigerate the remaining sauce.