Place a fine-mesh sieve over a medium heatproof bowl and set aside. In a medium saucepan, combine dark-brown sugar, cornstarch, and salt. In a medium bowl, whisk together milk, cream, and egg yolks; add to saucepan.
Whisking constantly, cook over medium-high until mixture thickens and is bubbling, 8 to 12 minutes. Reduce heat to medium-low and cook, whisking, 1 minute.
Remove pan from heat and pour mixture through sieve into bowl. Stir in butter and vanilla until combined.
Press plastic wrap directly against surface of pudding to prevent skin from forming and refrigerate 3 hours (or up to 3 days). To serve, whisk until smooth and divide among four small bowls.
Top with whipped cream. Make sure cream is cold before beating and add a little confectioners' sugar.