Prepare the impregnation. Dissolve sugar in warm boiled water, cool, add cognac.
Prepare a sponge cake. Beat eggs with sugar with a mixer. Sift flour and cornstarch, add in parts, stirring gently with a silicone spatula. Bake in a pan with parchment on the bottom. Bake for 25-40 minutes, depending on the oven, do not open the oven door for the first 20 minutes. Check readiness with a wooden skewer or toothpick. Cool the finished biscuit, put it in a bag or wrap it in cling film and leave it in the refrigerator overnight.
Prepare the cream. Combine eggs, sugar and cornstarch, mix thoroughly so that there are no lumps. Add hot cream and cook in a saucepan over medium heat, stirring vigorously until the mass thickens, then reduce the heat, add vanilla sugar, cook, stirring, for another 1-1.5 minutes. Immediately transfer the resulting mass into a glass or ceramic bowl, cover with cling film, cool at room temperature and leave in the refrigerator overnight. When the custard has stabilized, beat the butter with a mixer until white, add the custard base one spoon at a time, mixing well each time with a mixer until smooth.
Assemble the cake. Cut the biscuit into 3 layers. Soak the first cake layer, spread it with cream using a pastry bag, place the second cake layer, repeat the same 3 times. Cover the assembled cake with cream on all sides so that there are no dry spots or crumbs left.
Decorate the cake. Melt the chocolate. Using a piping bag, apply the design to the acetate film; when the chocolate begins to harden, place the design film on the sides of the cake and press. Place the cake in the refrigerator for 15-20 minutes, then carefully remove the film. Decorate the top of the cake with the remaining cream or confectionery.
Cut the cake into portions. Serve garnished with mint sprigs or berries.