Peel, core, and thinly slice the apples, then toss them with lemon juice to keep their color bright.
In a large mixing bowl, whisk together the flour, baking powder, cinnamon, and salt to evenly combine the dry ingredients.
In a separate bowl, beat together the granulated sugar, brown sugar, and melted butter until the mixture is smooth and slightly fluffy.
Add the eggs one at a time to the sugar mixture, beating well after each addition, then mix in vanilla extract until the batter is silky.
Gradually fold the dry ingredients into the wet mixture, mixing gently until just combined and smooth.
Gently fold in the sliced apples, distributing them evenly throughout the batter.
Pour the batter into a greased 9-inch cake pan, spreading it out evenly with a spatula.
Bake in a preheated oven at 350°F (175°C) for about 40 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
Slice the cake once cooled and enjoy its tender crumb with hints of cinnamon and soft apple pieces throughout.