Preheat your oven to 350°F (180°C or 160°C for a fan-assisted oven). Lightly grease an 8-inch round cake tin and line the bottom with a circle of parchment paper to ensure a clean release.
In a large mixing bowl, combine the softened butter and dark soft brown sugar. Using a wooden spoon or an electric hand mixer, beat the mixture vigorously for 2 to 3 minutes until it turns pale, light, and fluffy.
Add the room-temperature eggs to the butter mixture one at a time. Beat thoroughly after each addition until the egg is completely integrated before dropping in the next to keep the emulsion from splitting.
Add the self-raising flour and ground cinnamon straight into the wet base. Use a wooden spoon or silicone spatula to carefully fold the dry ingredients into the batter just until the flour disappears. Stop immediately to avoid over-activating the gluten grids, which can make the cake tough.
Add the 2 tablespoons of whole milk and stir in very gently to loosen the batter consistency slightly.
Prepare your apple: peel it completely and cut it away from the core. Slice half of the apple into thin, uniform wedges for the topping. Chop the other half into small pieces roughly ¼-inch wide.
Drop the small, chopped apple pieces directly into your cake batter and fold gently with a spatula to distribute them evenly through the matrix.
Tip the thick cake batter straight into your prepared tin, using the back of a spoon or spatula to smooth the surface flat and push it into the corners.
Arrange the reserved apple slices decoratively across the top of the batter. Take the extra tablespoon of dark brown sugar and sprinkle it uniformly over the apple slices to guarantee a crisp, sweet crust.
Place the tin on the middle oven rack and bake at 350°F for 25 to 30 minutes. The cake is finished when a wooden skewer or toothpick inserted into the exact center comes out clean.
Allow the cake to cool down flat inside the tin for 10 minutes. Run a thin knife along the inside edge to loosen the sides, remove the cake from the pan, and transfer it to a wire cooling rack. Serve warm alongside a scoop of vanilla ice cream or a pour of warm custard.