Preheat your oven to 350°F (175°C). Grease your baking pan and set aside.
Peel, core, and thinly slice the apples. Place them in a saucepan with brown sugar and cinnamon, then cook over medium heat until they become tender and caramelized, about 8-10 minutes. Stir occasionally and watch for a golden, sticky syrup coating the slices.
In a large mixing bowl, whisk together the eggs, sugar, vanilla extract, and melted butter until smooth and slightly frothy.
Gradually add the sifted flour and toasted sesame seeds to the wet mixture, folding gently until just combined. Be careful not to overmix to keep the batter light.
Pour the batter into the prepared baking dish and spread evenly with a spatula.
Arrange the caramelized apple slices on top of the batter in an appealing pattern, slightly pressing them down so they embed into the batter.
Bake the cake in the oven for about 40 minutes, or until the top is golden brown 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, then transfer to a wire rack or serve directly from the pan to enjoy the warm, caramelized aroma.
Slice the cake to reveal the tender apple slices nestled within the moist, sesame-infused crumb. The caramelized apples top the cake with a glossy finish.