Set the oven to 350 degrees Fahrenheit (175 degrees C). Use nonstick cooking spray and parchment paper to line a 6.5-inch springform pan. Use nonstick cooking spray to coat parchment paper.
Mix the lime juice with the apples and leave aside. In a bowl, combine the flour, salt, cinnamon, and ginger.
In a separate bowl, mash the eggs with the brown sugar, white sugar, and vanilla extract until smooth. Add the dry ingredients and blend just enough. About one-third of the batter should be poured into the pan. Top with remaining batter, then add apples.
Bake in the preheated oven for 50 to 60 minutes, or until a toothpick inserted in the centre comes out clean. After transferring, allow to cool for 15 minutes on a wire rack.
After releasing the springform pan with a knife, flip Apple Charlotte onto a plate. Place the cake on a serving plate right away.