Preheat oven to 375℉ and grease a 8x11 inch baking dish.
In a small bowl, combine the flour, baking powder, cinnamon, nutmeg and cardamom. Set aside.
In a mixing bowl, use a wooden spoon to mix the brown sugar, white sugar and melted butter together. Add the beaten egg and vanilla extract and mix until sugar mixture is wet. Slowly add the set aside dry ingredients and mix until just wet. Fold in the apples.
Pour the apple mixture into the set aside baking dish and put it in the oven for 20-25 minutes. Remove from the oven when the top is brown. Let cool for 10 minutes.
To prepare an apple cake sundae, place 2 spoonfuls of apple cake in a bowl. Top with a scoop of vanilla ice cream and drizzle caramel on top.