Combine first 3 ingredients in a medium saucepan. Bring to a boil over medium heat, stirring constantly with a whisk. Boil 2 minutes, stirring constantly. Remove from heat. Add chopped chocolate and vanilla, stirring with a whisk until chocolate melts. Cool 5 minutes.
Spoon 1/2 cup pudding into each of 8 individual serving bowls. Serve warm, or cover surface of pudding with plastic wrap, and chill thoroughly. Top each serving with whipped topping, if desired; sprinkle with chocolate shavings, if desired.