Preheat oven to 320 degrees F (160 degrees C). Grease a 9-inch square baking dish.
Beat eggs and 3/4 cup plus 2 tablespoons sugar in a large bowl using an electric mixer fitted with the whisk attachment until smooth. Carefully add 1/2 cup plus 3 tablespoons flour, ground walnuts, and baking powder; mix batter thoroughly until there are no lumps. Pour batter into the baking dish.
Bake cake in the preheated oven until barely set, about 5 minutes. Increase oven temperature to 375 degrees F (190 degrees C) and bake until golden, 25 to 30 minutes. Let it cool for a few minutes in the baking dish before transferring it to a wire rack to cool completely, about 45 minutes.
Beat butter, 1/2 cup white sugar, and egg yolk together in a bowl with the electric mixer until creamy and smooth. Add cocoa powder to cream filling and mix to combine.
Cut the cooled cake carefully in half horizontally. Place one layer on a serving plate and spread half of the cream filling on it. Top with the second layer. Scoop the rest of the filling onto the cake and smooth evenly over the top, letting excess filling drip down the sides.