Wash, peel, and cut the apples into large chunks. Toss the chopped apples with the juice from half a lemon to prevent them from browning while you prepare the batter.
In a large mixing bowl, whisk the 1/2 cup unsalted butter at room temperature with 1/2 cup superfine sugar until light and creamy. Add the eggs, incorporating them one at a time and mixing well after each addition. In a separate bowl, combine the flour and baking powder. Gradually add the dry mixture to the wet ingredients, mixing until the batter is soft and creamy. I like to make sure my butter is really soft—this makes the batter extra fluffy.
Line the bottom of a round baking tin with parchment paper. Grease the sides with butter and dust them with flour to prevent the cake from sticking.
Pour the cake batter into the prepared baking tin and spread it evenly. Arrange the apple chunks from Step 1 on top of the batter, gently pressing them down into the mix.
Melt 1/4 cup unsalted butter together with 1/4 cup superfine sugar in the microwave, stirring until smooth. Pour this mixture evenly over the apples on the cake. For a truly golden, caramelized top, I always make sure the topping is well mixed before drizzling.
Bake the assembled cake in a preheated oven at 355°F (180°C) for 1 hour, or until a toothpick inserted into the center comes out clean and the top is golden brown.
Allow the cake to rest for 10 minutes after baking. Carefully run a spatula along the edge to loosen the sides, remove the ring, and transfer the cake to a serving dish, peeling away the parchment paper from the bottom. Serve warm or at room temperature.