Preheat oven to 350 F/175 C.
Use a food processor to blend together walnuts with 1/3 cup brown sugar until you have a very finely ground walnut mixture.
In a bowl crack and beat egg whites until soft peaks, then add slowly the walnut sugar mixture into the egg whites. Divide the mixture into 4 equal parts.
Place a baking paper at the bottom baking dish and brush with oil and put one of the mixture parts on top. Bake for 15 minutes then repeat the process for the rest of the mixture parts.
Leave the baked layers aside and let them cool.
In a medium sauce pan melt the butter and mix it with cocoa.
Use a large bowl to beat egg yolks and ⅓ brown sugar until thick then add the melted cocoa mixture and continue whisking slowly adding the heavy cream.
Use a large round plate and place one of the layers then spread some of the mixture over it. Repeat the process with the rest of the layers and spread on top with chocolate mixture.
Cover the cake and place in the fridge for a few hours.