Preheat and prepare your tin. Set your oven to 180°C (fan-assisted). Grease a 23cm springform cake tin with a little butter, then line the base with a circle of baking parchment. The sides don't need lining — the springform will release the cake cleanly, and the exposed edges will develop a lovely golden crust.

Cream the butter and sugar. Place the softened butter and caster sugar in a large mixing bowl. Beat with an electric mixer on medium speed for 3–4 minutes, until the mixture turns pale, fluffy, and almost doubled in volume. It should look like soft, airy clouds — if it still feels gritty, keep beating. The sugar needs to dissolve into the butter for a tender crumb.

Add the eggs and vanilla. Crack the eggs into a small jug and add the vanilla extract. With the mixer running on low, add the eggs one at a time, waiting until each is fully incorporated before adding the next. The batter will look smooth and glossy, and it should smell sweetly of butter and vanilla. If it looks like it's separating, add a tablespoon of the flour from the measured amount — this will bring it back together.

Combine the dry ingredients. In a separate bowl, whisk together the plain flour, baking powder, bicarbonate of soda, and salt. This ensures the raising agents are evenly distributed, so your cake rises uniformly without any bitter pockets.

Fold the flour and yoghurt into the batter. Add half the flour mixture to the butter mixture and fold gently with a spatula until just combined. Add the yoghurt and the squeeze of lemon juice, fold again, then add the remaining flour. Fold only until you can't see any streaks of white — overmixing will develop the gluten and make the cake tough. The final batter should be thick, smooth, and drop easily from a spoon.

Prepare the plums. While the batter rests for a minute, halve your plums and remove the stones. If your plums are very large, cut each half into two wedges. Toss them gently in a bowl with the lemon juice to prevent browning — this also brightens their flavour.

Assemble the cake. Spoon the batter into the prepared tin and spread it evenly with the back of a spoon. Arrange the plum halves on top, cut-side up, in concentric circles starting from the outside edge. Press them gently into the batter — they'll sink slightly as the cake bakes, creating that beautiful, sunken look. Sprinkle the demerara sugar evenly over the top. This will caramelise into a crisp, golden crust.

Bake and observe. Place the tin in the centre of the oven and bake for 40–45 minutes. At the 30-minute mark, the kitchen will fill with the warm, fruity scent of caramelising plums and butter. The cake is done when a skewer inserted into the centre (avoiding a plum) comes out clean or with a few moist crumbs. The top should be deep golden brown, and the edges will have pulled slightly away from the tin.

Cool and serve with flair. Let the cake cool in the tin for 15 minutes. The plums will have released their juices, creating a gorgeous, glossy surface. Run a knife around the edge, release the springform, and transfer to a wire rack. For a restaurant-style finish, dust lightly with icing sugar just before serving. The contrast of white snow against the dark purple plums is stunning.