6 tablespoons unsalted butter, divided
1/3 cup dark brown sugar
2 medium-sized firm apples
1 cup all-purpose flour
1/2 teaspoon cinnamon, plus extra for the apples
1/2 teaspoon cloves
1/2 teaspoon ground ginger
1/2 teaspoon cardamom
1/2 teaspoon salt
1 teaspoon baking powder
1/2 cup milk
2 eggs
1 cup sugar
Preheat the oven to 375°F. Melt 4 tablespoons of the butter in a small saucepan over low heat. Add the brown sugar and stir until well-combined. Let it bubble for about 2 minutes, then remove from the heat and spread in the bottom of a 9-inch round cake pan. Set aside.
Peel the apples and core them. Cut them in thick slices, and cut each slice in half. Arrange the apples cut-side up in the prepared pan. Sprinkle them lightly with cinnamon.
Whisk together the flour, cinnamon, cloves, ginger, and cardamom, as well as 1/2 teaspoon salt and 1 teaspoon baking powder. Warm the milk in a small saucepan set over medium heat. Add the remaining 2 tablespoons butter and keep warm until the butter melts completely.
While the milk is warming, beat the eggs for 3 to 5 minutes, or until they are very thick and pale. Gradually add the sugar and beat for 5 minutes. Add the flour mixture, and then the hot milk. Stir until the batter is smooth, and pour it over the apple.
Bake for about 40 minutes, or until the cake is golden. Let the cake cool for a full 10 to 15 minutes, then run a knife around the inside of the pan to help release the cake, and invert onto a serving plate.
Serve with vanilla ice cream or whipped cream.