In a medium bowl, whisk together the egg yolks, cornstarch, and 1/2 cup of the milk until completely smooth.
In a medium saucepan, combine the remaining milk, heavy cream, espresso, brown sugar, granulated sugar, caramel sauce, salt, and espresso powder.
Heat over medium heat, whisking occasionally, until the mixture is steaming and the sugars have dissolved. Do not boil.
Slowly whisk about 1 cup of the hot mixture into the egg mixture to temper the eggs.
Gradually whisk the tempered egg mixture back into the saucepan.
Cook over medium heat, whisking constantly, until the pudding thickens and begins to bubble.
Continue cooking for 1 minute after bubbling begins to fully activate the cornstarch.
Remove from the heat and whisk in the butter and vanilla extract until smooth.
Strain the pudding through a fine-mesh sieve into a clean bowl for the silkiest texture.
Divide evenly among six ramekins or dessert glasses.
Press plastic wrap directly onto the surface of each pudding.
Refrigerate for at least 4 hours or overnight until fully chilled and set.
Top with whipped cream, a drizzle of caramel sauce, and chocolate-covered espresso beans before serving.