Preheat the oven to 350 degrees F (175 degrees C). Line the bottom of a 10-inch nonstick springform pan with parchment paper.
Soak 1/2 cup plus 1 tablespoon chia seeds in coffee for 15 minutes.
Meanwhile, melt chocolate chips and butter in a double boiler. Let cool.
Beat egg whites and 1/3 cup sugar with an electric mixer in a mixing bowl until soft peaks form. Set aside.
Beat egg yolks, vanilla, and remaining sugar in a separate bowl with an electric mixer until pale and creamy. Fold in the melted chocolate mixture. Fold in soaked chia seeds, hazelnuts, and cappuccino mix. Stir in egg white mixture. Pour into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 50 minutes. Let cool completely in pan, at least 1 hour, before transferring to a wire rack with a parchment paper-lined baking sheet underneath to catch excess during coating.
Meanwhile, melt dark chocolate, instant espresso powder, and shortening in a double boiler. Pour over cooled cake, coating top and sides evenly. Let cool until set.
While the coating sets, beat whipped cream, coffee-flavored liqueur, and cappuccino mix together with an electric mixer until stiff peaks form. Use to pipe desired designs on cooled cake.
