Add the sugar, cornstarch, cocoa powder, espresso powder and salt to a large saucepan with a curved bottom; whisk to remove any lumps. Pour in the milk, heavy cream, vanilla bean seeds and egg yolks, and whisk again until smooth and well mixed.
Set the saucepan over medium heat and cook, whisking, until the mixture is thick enough to coat the back of a wooden spoon, 6 to 8 minutes. (While whisking, make sure to pay attention to the bottom and sides of the saucepan.) Add the semisweet and bittersweet chopped chocolate and stir to melt.
Pour the now thickened pudding through a fine mesh sieve into a 4-cup measuring cup. Divide the pudding between six 6-ounce glass jars or serving cups. Cover with plastic wrap, pressing against the surface of each pudding to keep a skin from forming. Refrigerate until thoroughly chilled and set, at least 3 hours.
Serve the budino topped with freshly whipped cream and shaved chocolate.
Add the cream to a large bowl and beat with an electric hand mixer until thick as melted ice cream. Sprinkle in the confectioners' sugar, add the vanilla bean seeds, and continue to whip until soft peaks appear.