Add the heavy whipping cream, sugar, cocoa powder, and butter to a medium saucepan. Whisk until combined.
Place over medium-low heat. Whisk continuously until the sugar dissolves and the mixture comes to a gentle simmer.
Once simmering, continue cooking for 5 minutes, keeping the heat low and whisking as it simmers.
Remove the saucepan from the heat. Add the chopped dark chocolate, salt, and vanilla extract.
Whisk until the chocolate has completely melted and the sauce is smooth and glossy.
Allow the sauce to cool slightly before serving. It will thicken as it cools. Transfer to an airtight container and refrigerate for up to 2 weeks. Gently reheat before serving.