Preheat your oven to 350°F (175°C). Grease a 7-inch square cake pan and line it with parchment paper for easy removal. In a small saucepan, gently melt the butter and set it aside to cool slightly after removing it from the heat.

In a large bowl, whisk together the eggs and sugar until the mixture becomes pale, thick, and mousse-like. It should be thick enough that when you lift the whisk, the mixture leaves a visible trail behind.

Sift together the flour, cornstarch, baking powder, and salt. Carefully fold half of this dry mixture into the egg mixture. Once combined, gently pour half of the cooled butter around the edge and fold it in. Repeat this step with the remaining flour and butter, taking care not to deflate the batter.

Pour the batter into the prepared pan, smoothing the top with a spatula. Bake for 35–40 minutes, or until the cake has risen and springs back when lightly pressed. Let the cake cool in the pan for a few minutes, then turn it out onto a wire rack to cool completely, removing the parchment paper.

To make the chocolate filling, melt the dark chocolate in a heatproof bowl set over a pan of simmering water. Stir occasionally until smooth, then remove from heat and set aside to cool.

In a small saucepan, combine the sugar and water. Heat gently until the sugar dissolves, then bring it to a boil. Let it boil for about 5 minutes until the syrup forms a slim thread when pulled apart between two teaspoons.

Place the egg yolks in a separate bowl and whisk lightly. Slowly pour the hot syrup in a thin stream onto the yolks, whisking constantly. Continue whisking until the mixture thickens and cools. In another bowl, beat the softened butter until smooth and creamy, then gradually add the cooled egg mixture. Stir in the cooled, melted chocolate until fully combined.

Once the sponge is completely cool, slice it horizontally into two even layers using a serrated knife. Spread a thin layer of the chocolate buttercream over the bottom half, then place the top half back on. Trim any uneven edges and cut the sponge into 2¼-inch squares.

Spread the remaining chocolate buttercream over the top and sides of each square. Press the finely chopped, toasted mixed nuts around the edges for a crunchy texture. Finally, pipe small decorative rosettes of the remaining buttercream on top of each square for a polished look.