Preheat oven to 350˚F (180˚C). Grease a 9 inch (23 centimeter) springform pan or cake pan with butter.
Separate the four eggs into whites and yolks.
Beat the egg whites in a stand mixer with a whisk attachment until stiff peaks form.
In another bowl, combine the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, combine the sugar and orange zest. Beat with the butter until light and creamy.
Beat in the egg yolks, one at a time, until incorporated.
Slowly beat in the orange juice, followed by the brandy and vanilla extract.
Fold in 1/3 of the beaten egg whites, followed by 1/3 of the flour mixture.
Continue with another 1/3 egg whites, 1/3 flour, then remaining egg whites and remaining flour just until no streaks remain. Take care to not deflate the egg whites.
Transfer the batter to the prepared pan.
Bake in the preheated oven until the edges are golden brown and a toothpick inserted in the center comes out clean, 35-40 minutes. Do not open the oven door until the cake is nearly done.
Allow to cool to room temperature before decorating and dusting with a layer of powdered sugar.