Preheat the oven to 350 degrees F (175 degrees C). Spray a 6½-inch springform pan with nonstick cooking spray and line with parchment paper. Spray parchment paper with nonstick cooking spray.

Add the lime juice to the apples and toss; set aside.

In a separate bowl, mix together the flour, cinnamon, cardamom, ginger, and salt in a bowl and set aside.

Using an electric mixer, add the eggs with brown sugar, white sugar, and vanilla extract in a bowl and beat until creamy. Add in the dry ingredients and mix until just combined. Pour about 1/3 of the batter into the prepared pan. Add apples and top with remaining batter.

Bake until a toothpick inserted in center comes out clean, 50 to 60 minutes. Transfer to a wire rack and cool for 15 minutes.

Next, take a knife and run it around the inside of the springform pan, then release the springform. Flip apple Charlotte onto a plate or serving platter. Allow to sit for about 15 minutes, then dust with powdered sugar.

Slice and serve warm with vanilla whipped cream or vanilla ice cream cream.