Pour hot milk over ground walnuts to obtain a thick, creamy paste.
Cream the butter, add walnut paste and mix some more until the mixture is uniform.
Whisk the egg whites into stiff peaks adding slowly the icing and vanilla sugar. Fold the egg whites into the walnut cream by hand so it evens out.
To assemble the cake divide the walnut filling into 7 equal parts (use seven equal cups or small bowls).
Take a large serving tray and place the first cake crust on it. Sprinkle with a little warm milk (but very sparingly) and immediately spread the 1/7th of the filling over it. Cover with the next layer, sprinkle with milk and spread the filling. Repeat with the remaining crusts, save the best one for the top.
Place parchment paper over the top layer, weigh the cake down with a heavy object (large, full tins, milk bricks and such). Leave in a cold place for at least 12 hours. Take the cake out of the fridge and bring to the room temperature (at least 3 hours) before glazing.
For the pink glaze whisk the egg whites into stiff peaks. Set 2-3 tablespoons of the beaten egg whites aside for later.
Add the icing sugar, lemon juice, sunflower oil and food coloring and whisk until the mixture is thick and shiny. If the mixture is too dry add the saved egg whites.
Run under hot tap water long and wide knife and spread evenly the glaze on the top crust. Place the cake in the fridge for couple of hours so the icing can harden.