Warm the milk and cream in a small saucepan over medium-low heat until small bubbles form around the edges—do not boil.

Stir in the sugar and vanilla extract, whisking gently to combine.

Add the chopped dark chocolate and let it sit for 30 seconds to soften. Whisk until the chocolate is fully melted and smooth.

Continue cooking on low heat for 3–5 minutes, whisking constantly, until the mixture thickens to a velvety consistency that coats the back of a spoon.

Pour the hot chocolate into mugs and top with whipped cream or chocolate shavings if desired. Serve immediately.