Preheat the oven to 175 °C (350 °F). Beat the egg white to stiff peaks and fold in the hazelnuts and flour with a spatula. Spread the mixture evenly on a piece of parchment paper, creating a circle 18 cm in diameter. Bake for 13 minutes. Carefully peel the baked hazelnut base off the parchment paper and cool on a cooling rack.
While the hazelnut base is in the oven, prepare the sponge. Beat the egg and sugar for 10 minutes. Sift the cocoa and flour on top of the egg mixture and fold in gently with a spatula. Spread the mixture evenly on a 16 cm cake pan lined with parchment paper (the bottom), and bake for 10 minutes at 180 °C (350 °F). After a few minutes, take the baked sponge out of the pan and allow to cool on a cooling rack.
Whip the whipping cream and refrigerate; soak the gelatin in cold water for 5 minutes. Mix the mascarpone cheese with the pistachio spread, vanilla, sugar and food coloring until smooth. Heat the milk and use it to dissolve the wrung-out sheets of gelatin. Add it to the filling and mix well. Finally, fold in the whipped cream using a spatula.