Cut the apples into large chunks. Mix them with the juice from half a lemon to prevent them from browning. Set aside until ready to use.
In a large bowl, whisk 1/2 cup unsalted butter at room temperature with 1/2 cup caster sugar until light and fluffy. Add the eggs, one at a time, beating well after each addition. In a separate bowl, mix the all-purpose flour with the baking powder. Gradually add the flour mixture to the wet ingredients, mixing just until a soft and creamy batter forms. I like to make sure not to overmix at this stage to keep the cake tender.
Line the bottom of a round baking tin with parchment paper. Butter and coat the sides with flour. Pour the cake batter into the prepared tin and spread evenly. Arrange the lemon-tossed apple chunks from Step 1 over the cake batter, pushing the apples down gently into the mix.
Melt 1/4 cup unsalted butter and 1/4 cup caster sugar together in the microwave until smooth and combined. Pour this mixture evenly over the apples and cake batter in the tin. This step gives a beautiful, sweet crust to the top of the cake.
Bake the assembled cake in a preheated oven at 355°F (180°C) for 1 hour, until the top is golden and a skewer inserted into the cake comes out clean. Allow the cake to rest for 10 minutes in the pan after baking before proceeding.
After resting, use a spatula to carefully detach the apples and cake from the sides of the pan. Remove the ring, then transfer the cake to a serving dish, peeling away the parchment paper from the base. Serve the cake warm or at room temperature. For extra flavor, I sometimes dust the top with a little extra caster sugar just before serving.