Prepare the Pan and Oven: Preheat your oven to 350°F. Butter the bottom of a 9-inch springform pan and line it with parchment paper. Do not grease the sides of the pan, as the cake needs to "cling" to rise evenly. Set aside.
Mix the Eggs and Sugar: In the bowl of a stand mixer (or a large bowl with a hand mixer), beat the eggs on high speed for about 1 minute until frothy. Gradually add 1 cup of the sugar while continuing to beat for 6–8 minutes. The mixture should thicken and become pale, forming ribbons when drizzled back onto itself.
Combine Dry Ingredients: In a separate bowl, whisk together the flour, baking powder, and salt. Sift this mixture into the beaten eggs in three portions, folding gently with a spatula after each addition. Be careful not to overmix. Add the vanilla extract and fold just until incorporated. Set aside ½ cup of the apple slices for the topping, and fold the remaining apple pieces into the batter.
Assemble the Cake: Pour the batter into the prepared pan and smooth the surface with a spatula. Arrange the reserved apple slices evenly over the top in a single layer. Place the pan in the oven and bake for about 60 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Add Cinnamon Sugar Topping: Once the cake is baked, let it cool in the pan for 15 minutes. While it cools, mix the remaining 1 tablespoon of sugar with the cinnamon. Run a thin knife or spatula along the edges of the cake to loosen it, then carefully remove the springform collar. Sprinkle the cinnamon-sugar mixture evenly over the top.
Cool Completely: Transfer the cake to a serving plate and let it cool completely before slicing. This allows the flavors and texture to set properly.