1. Preheat oven to 350 degrees (F).
2. Prepare a 9×9 baking pan with cooking spray and parchment paper. Allow flaps of parchment to hang over the side of the pan to help with removal. Set aside.
3. In a small bowl, sift together flour, baking powder and salt.
4. In another bowl, toss chopped apples with lemon juice.
5. In a small bowl, whisk together brown sugar, cardamom and cinnamon. Pour over apples and stir to thoroughly coat. Set aside.
6. In a large bowl, combine butter, cream cheese and granulated sugar, and beat until light and fluffy. Add eggs, one at a time and beat each until fully incorporated. Add vanilla, and beat to combine.
7. Slowly add dry ingredients, beating until just incorporated. Don’t overbeat.
8. Use a spatula to fold the apples into the batter.
9. Pour batter into prepared pan and spread evenly.
10. Bake until the top is golden brown, about 60-70 minutes.
11. Check done-ness with a cake tester or toothpick, it should come out clean. If cake gets too dark on top, you can cover it with foil for the last 15 minutes or so.
12. Allow to cool on a wire rack in the pan for 10 minutes.
13. Use parchment paper flaps to lift cake out of the pan, and place on a wire rack.
14. Place the wire rack and cake over a baking sheet or a piece of parchment paper before icing to catch drips.

For glaze:

1. Combine powdered sugar, milk and vanilla in a small bowl and whisk to combine. Add more milk a few drops at a time if necessary, to reach a smooth and pourable consistency.
2. Pour over warm cake.