Chop Chocolate. To start, finely chop the chocolate into very small pieces. The smaller you chop the chocolate, the easier it will melt!
Combine Cream Mixture. In a small saucepan, combine heavy cream, whole milk, and powdered sugar. Heat over medium-high heat until it's steaming, but not yet simmering or boiling.
Melt Chocolate. When the cream mixture is steaming, stir in the chopped chocolate and stir over medium heat or medium-low heat to melt. A whisk is a great option here!
Adjust The Texture, If Needed. If your chocolate isn't melting perfectly smoothly, an immersion blender or even a milk frother can help. It usually only takes 1-2 pulses to immediately make the mixture smoother! Finish With Vanilla. Stir in the vanilla extract.
Serve & Store. Enjoy hot with dollops of whipped cream and grated chocolate, as desired. Cool leftover French hot chocolate and store in a jar or an airtight container in the fridge 3-4 days. Reheat on the stove over medium-low heat, or in the microwave in 15-20 second intervals until heated through.