Preheat oven to 175°C / 350°F.
Prepare a 10-inch (26cm) round pan. Use either a plain baking pan or a Springform pan and grease with oil and flour or line with parchment paper.
Prepare the apples. Peel and finely chop the apples. Add them to a mixing bowl with 3 tablespoons of brown sugar, 2 tablespoons icing sugar, 2 tablespoons brandy, and 1 teaspoon ground cinnamon. Stir well to combine and set aside.
Combine flour and baking powder in a bowl.
Whisk to combine orange juice with olive oil, brown sugar (save 1½ tablespoons to sprinkle on top), ½ teaspoon ground cinnamon, cardamom, vanilla extract, salt, and baking soda.
Add the flour into the bowl with the wet ingredients, and whisk until uniform.
Stir in the walnuts and apples.
Transfer the cake batter to the prepared pan and spread evenly with a spoon. Sprinkle the reserved 1½ tablespoons of brown sugar on top.
Bake for 45 to 50 minutes (on the lowest rack) or until a toothpick inserted in the center of the cake comes out clean.
Allow the cake to cool down to room temperature.
Serve with icing sugar on top and some ground cinnamon.