In a small bowl, mix 1/4 cup sugar with cinnamon and set aside.
Line a loaf pan with parchment paper.
In a small pot, heat 1/4 cup sugar over medium heat until it turns into caramel (do not stir with a spoon; you can gently tilt the pot to mix). Pour the caramel onto the parchment paper in the pan and spread it evenly. Arrange two layers of apple slices over the caramel and sprinkle with some of the sugar-cinnamon mixture. Add two more layers of apples, press down firmly with your hands, and sprinkle again with the sugar-cinnamon mixture. Repeat with all the apple slices.
Preheat the oven to 355°F (180°C) and bake for 45 minutes.
Remove the cake from the oven, flip the pan onto a tray, peel off the parchment paper, and slice thinly.