Preheat the oven to 338°F (170 °C). Place baking paper in an elongated tray and gently grease it. Mix the flour, salt, baking powder and baking soda in a bowl. In another bowl, mix the banana puree, 2/3 cup of sugar, 3 tablespoons of oil, eggs, the vanilla, nutmeg. Beat this mixture with the flour one.
Blend the cake mix carefully with the walnuts and divide it in 2. Color one part with the cocoa. Bake both layers successively in the prepared tray. Using a sharp knife, cut thin slices of equal length. Combine the brown sugar, water and butter in a small pot on the stove and bring them to a boil.
Stir for 1 minute and remove from the heat. Assemble the thin sponge cake pieces in a chess pattern using this sauce as glue. Alternate brown and white strips in a few rows, until you run out of strips. If any sauce is left, pour it over the chess sponge cake.