Heat the oven to 320°F (160°C) convection. Line the base of a 9-inch/22 cm ring mold or springform pan with foil and parchment paper. Lightly grease the sides.
In the bowl of a stand mixer fitted with the whisk attachment, whip the egg whites with the sugar on medium-high speed until stiff but not dry, 2 to 3 minutes. Reduce speed to low and beat in the yolks and oil just until combined. Remove the bowl from the mixer.
Using a rubber spatula, fold in the coconut, walnuts, and grated chocolate. Sprinkle in the potato starch, baking powder, and coffee powder, and fold gently until the batter is uniform and no streaks remain.
Scrape the batter into the prepared pan and smooth the top. Bake until a toothpick inserted in the center comes out with moist crumbs, 25 to 30 minutes.
In a small saucepan, combine the sugar, water, and coffee powder. Bring to a simmer over medium heat, stirring just until the sugar dissolves. Remove from the heat and let cool.
Remove the cake from the oven and immediately pierce it all over with a fork or skewer. Brush the entire surface with the coffee syrup, using all of it—this step ensures the cake stays moist. If the center sinks slightly, it’s fine.
Let the cake cool completely at room temperature or refrigerate until cold.
Combine the heavy cream, pudding mix, powdered sugar, and coffee powder in the clean bowl of a stand mixer fitted with the whisk attachment. Whip on medium-high speed until thick and spreadable, 2 to 3 minutes.
Spread the cream over the cooled cake in an even layer. Top with shaved chocolate and refrigerate for at least 6 hours or overnight before serving.