In a small saucepan, bring milk just to a boil over medium heat. Whisk in chocolate and sugar until blended. If necessary, cook over low heat, stirring constantly, until completely smooth and heated through. (Do not allow to boil). Stir in vanilla extract. Divide among demitasse, espresso, or tea cups; serve immediately.
Notes
Note: For easy pouring, the hot chocolate can be made in a 4-cup glass measuring cup using a microwave.
Recipe by Victoria at https://victoriamag.com/parisian-hot-chocolate-recipe/