Whisk together the sugar, cornstarch, salt, egg, and egg yolk in a medium saucepan. Whisk in the cream.
Cook over medium heat, stirring continuously with a wooden spoon, until thickened and steadily boiling, 8 to 10 minutes. Remove from heat and stir in the butter and vanilla until the butter melts.
Divide among serving bowls or glasses. Spoon the blackberries on top. Cover with plastic wrap and refrigerate until well chilled, at least 1 hour and up to 2 days.
Serve topped with the whipped cream.