Preheat oven to 350°F.

Grease and flour a 9-inch round springform pan or a 9 x 9-inch square baking pan or baking dish.

To Make the Cake: In a bowl, stir together the flour, baking powder and salt.

In another bowl, toss the apples with the juice.

In a small bowl, stir together the brown sugar, cardamom and cinnamon.

Add to the apples and toss to coat.

Set aside.

In the bowl of an electric mixer fitted with the flat beater, combine the butter, cream cheese, granulated sugar and vanilla and beat on medium speed until light and fluffy. Add the eggs, one at a time, beating well after each addition.

Add the flour mixture in 2 or 3 additions and beat well until smooth.

Using a large rubber spatula, gently fold in the apples just until evenly distributed, no more than a few strokes.

Do not overmix.

Spoon the batter into the prepared pan and spread evenly.

Bake until the top is golden brown and a toothpick inserted into the center of the cake comes out clean, 60 to 70 minutes. Transfer the pan to a wire rack and let cool for 5 minutes.

To Make the Glaze: In a small bowl, whisk together the confectioners’ sugar, the 2 tablespoons milk and the vanilla until smooth and pourable.

Adjust the consistency of the glaze by adding more milk, a few drops at a time, if needed.

Remove the sides of the springform pan, if using, and place the cake on a wire rack set over a piece of waxed paper to catch any drips.

While the cake is warm, drizzle with the glaze.

Let the cake cool to room temperature.

Cut into wedges or squares to serve.