Preheat the Oven and Prepare the Tin: Preheat the oven to 170°C. Generously grease a 20 cm round loose-bottom or springform cake tin with butter, coating the base and sides. Set aside.
Cream the Butter and Sugar: Place the softened butter and golden caster sugar in a mixing bowl. Beat with an electric mixer for a couple of minutes until the mixture becomes pale and fluffy.
Prepare the Cake Batter: Add the egg and self-raising flour to the creamed butter mixture. Mix again until the ingredients are combined into a thick, sticky batter. This consistency is normal for the recipe.
Spread the First Layer of Batter: Spoon approximately two-thirds of the batter into the prepared cake tin. Use a fork or small offset spatula to spread it gently across the base, ensuring the bottom is completely covered.
Slice and Season the Apples: Cut the peeled and cored apples into slices approximately 1 cm thick. Place them in a large mixing bowl, add the 3 tablespoons of soft light brown sugar or demerara sugar and the ground cinnamon, then toss until the apple slices are evenly coated. Arrange the Apple Layer: Distribute all the seasoned apple slices over the batter in the tin, creating a generous, thick layer. Make sure the apples are spread across the surface.
Add the Apricot Jam: Place small dollops of apricot jam over the apples. Spread the jam roughly across the layer so that it is distributed throughout.
Cover with the Remaining Batter: Spoon the reserved batter over the apples and gently spread it using a fork or small offset spatula. It is fine if a few small gaps remain; the batter will spread as the cake bakes.
Sprinkle the Sugar Topping: Scatter 1 tablespoon of demerara sugar evenly over the top of the cake to create a sweet, lightly crisp finish.
Bake the Apple Cake: Place the tin in the preheated oven and bake for approximately 1 hour. The cake is ready when a toothpick inserted into the middle comes out clean and the apples are tender.
Cool Before Removing: Take the cake out of the oven and leave it to cool in the tin for 10 minutes. Carefully remove it from the tin afterward.
Finish and Serve: If desired, dust the cake with icing sugar before serving. Enjoy it warm or cold, either on its own or accompanied by clotted cream or a scoop of vanilla ice cream.