Preheat the oven to 350 degrees F (175 degrees C). Grease the bottom and sides of a square cake pan. Cut a piece of parchment paper to fit the base exactly and grease the paper.

Sift flour, cinnamon, cloves, anise, and cardamom together into a bowl.

Beat butter and vanilla extract together in a bowl using an electric mixer until creamy. Cream egg yolks and 1 cup plus 2 tablespoons sugar together in another bowl until thick and tripled in volume. Place egg whites in a separate bowl using clean beaters; mix until stiff peaks form.

Mix the creamed butter with the creamed egg yolk mixture. Slowly fold in the spiced flour, alternating with beaten egg whites. Carefully mix well.

Pour 1 ladleful of cake batter into the prepared pan. Spread batter evenly into a layer about 1/4-inch thick.

Bake in the preheated oven until light brown, about 5 minutes. Remove pan from oven; use a skewer to prick the top of the cake to prevent air bubbles from forming.

Spread another ladleful of batter on top and bake the new layer for about 5 minutes. Repeat the process and bake each remaining ladle of batter. When done, remove the cake from pan at once. Turn it over, top side up, onto a cooling rack and let cool for at least half an hour.