Place the chopped dark chocolate in a heatproof bowl. Heat 1 cup of heavy cream in a small saucepan over medium heat until it just begins to simmer, then pour over the chocolate. Let sit for 2 minutes, then whisk until smooth and glossy. Refrigerate for 30 minutes, stirring every 10 minutes, until thickened but still pourable.
While the chocolate mixture chills, whip the remaining 1 cup of heavy cream with 3 tablespoons powdered sugar and vanilla extract in a chilled bowl using an electric mixer on high speed until stiff peaks form, about 3-4 minutes. Set aside in the refrigerator.
In a small bowl, combine the cooled espresso with 2 tablespoons granulated sugar, stirring until the sugar dissolves completely. Set aside for soaking the cake cubes.
To assemble the trifle, arrange one-third of the cake cubes in the bottom of a 3-quart trifle dish or large glass bowl. Drizzle with one-third of the espresso mixture, allowing it to soak in for 1 minute.
Spoon half of the chilled chocolate mixture over the soaked cake layer, spreading gently to the edges. Top with half of the sweetened whipped cream, spreading evenly.
Repeat the layers: cake cubes, espresso soak, remaining chocolate mixture, and remaining whipped cream. Finish with a final layer of cake cubes and espresso.
For the topping, whip 1 cup of heavy cream with 2 tablespoons powdered sugar until stiff peaks form. Spread or pipe decoratively over the top layer of the trifle.
Dust the top with cocoa powder using a fine-mesh sieve, then garnish with chocolate shavings. Cover and refrigerate for at least 4 hours or up to 24 hours before serving to allow the flavors to meld and the cake to soften beautifully.