Preheat oven to 250 C / Gas 9. Line a baking tray with baking parchment.
For the cake: Beat together sugar and egg yolks until light and creamy. Stir in melted butter, then fold in 1/2 of the flour.
In a separate bowl, beat egg whites with 1 pinch salt until stiff. Gently fold in 1/2 egg whites into the yolk mixture, followed by the remaining flour and remaining egg whites. Mix gently.
Pour batter into prepared tray and smooth out to a 1cm thick layer. Bake in preheated oven for about 10 minutes.
Remove cake from oven and turn out onto a tea towel. Cut into two parts, one barely wider than the other (not more than 5mm). Slice a small strip from the widest cake and cool.
For the buttercream: Microwave chocolate with 1 tablespoon water in 10 second bursts. Stir after each burst until the chocolate is smooth and glossy.
In a food processor (or using a wooden spoon), beat butter until soft, then add icing sugar and chocolate. Stir in milk. Once cool, spread over one of the cakes, then carefully place the other cake on top. Add the strip of cake on the side to resemble the spine of a book.
To decorate: Microwave chocolate and a knob of butter until melted. Once melted, add remaining butter and stir until smooth and glossy. Spread all over the book cover. Do not put any on the sides, as this resembles the pages of the book.