In a medium bowl, whisk together evaporated milk, sugar, salt, and vanilla until combined. Transfer to the container of a blender, and process on medium speed until smooth and sugar is melted, about 30 seconds.

In the top of a double boiler, place chocolate, butter, and espresso powder. Cook over simmering water, until melted and smooth, stirring only when chocolate mixture is almost melted. Add to milk mixture; process on medium speed until thickened, shiny, and smooth, stopping to scrape sides of container, 30 to 45 seconds. Transfer to a medium bowl. Cover and refrigerate until cooled, about 15 minutes.