Beat egg whites to stiff peaks. Sift powdered sugar and fold in 1 tablespoon at a time. Set aside about 4 large tablespoons of this meringue.
Fold vanilla sugar, cinnamon, cardamom, and almonds (roughly 350-400 g) into the remaining egg whites until the dough barely sticks. Purée the cooked chestnuts (100 g) and knead into the dough with flour, orange peel, and 1 teaspoon cocoa powder. Form 4 rolls approximately 1 euro in diameter, wrap in cling film, and refrigerate for 2 hours.
Preheat oven to 130°C / 266°F (convection: 100°C / 212°F).
Remove rolls from refrigerator. Cut into slices approximately 1 cm thick, shape them, and place on a baking sheet lined with parchment paper.
Remove 2 teaspoons of the reserved meringue and mix with the remaining cocoa powder. Spread the light meringue mixture on each thaler, place a small drop of the dark cocoa meringue in the center, and draw a star pattern with a wooden stick.
Bake on the middle rack for 15 minutes at 130°C / 266°F. Reduce temperature to 100°C / 212°F (convection: 80°C / 176°F) and bake for another 15 minutes.