Place chopped chocolate in a large bowl with a fine mesh sieve over top.
Whisk egg yolks and sugar together in a medium bowl until creamy and fully combined, about 1 minute.
Heat the heavy cream over medium heat in a large saucepan until lightly simmering with small bubbles forming at the edge of the pan.
Slowly pour the heavy cream into the egg yolk and sugar mixture, whisking constantly. Return the mixture to the saucepan.
Cook over medium heat while stirring constantly and scraping the edges, bottom and sides of the saucepan until the mixture is thick enough to coat the back of the spoon, about 3 minutes or until an instant read thermometer reads 175 degrees
Pour the custard through the fine mesh sieve over the chocolate.
Stir the custard into the chocolate until the chocolate is fully melted.
Stir in vanilla, butter and salt until combined.
Divide the budino evenly into 8, 6-8 oz ramekins filling about ⅔ full. Cover with plastic wrap.
Refrigerate for 4 hours before serving.