In a medium bowl, whisk together 1/2 cup sugar, the cocoa powder, cornstarch and salt. Whisk in 1/2 cup milk.
In a large saucepan, bring 1 1/2 cups cream and the remaining 1 1/2 cups milk and 1/4 cup sugar to a simmer over medium heat, stirring occasionally. Stir in the bittersweet chocolate, slowly whisk in the cocoa mixture and cook, whisking, until thickened, about 5 minutes; whisk in the vanilla. Transfer the pudding to a medium bowl. Cover the surface of the pudding with plastic wrap and refrigerate for 2 hours.
Meanwhile, in a small saucepan, melt the white chocolate in 1/4 cup cream, stirring frequently, over low heat; let cool.
Using an electric mixer, whip the remaining 1 cup cream until soft peaks form. Whisk about 1/2 cup of the whipped cream into the white chocolate. Fold the white chocolate mixture into the remaining whipped cream; refrigerate.
Spoon about 1/4 cup of the chilled chocolate pudding into each of 6 parfait glasses. Top with about 3 tablespoons of the white chocolate whipped cream. Repeat to make a total of 4 layers. Serve immediately or cover and refrigerate for up to 6 hours.