Preheat the oven to 155°C (310°F)/fan 135°C (275°F)/gas mark 2. Lightly oil four muffin moulds.
To make the tomato and rosemary cakes, whisk the eggs, oil, and tomato purée in a large mixing bowl.
Add the sifted flour, rosemary, and salt, mixing until thoroughly combined.
Divide the batter evenly between the prepared muffin moulds.
Bake for 20–25 minutes, or until a skewer inserted into the centre comes out clean.
Let the cakes rest in the moulds for 10 minutes before carefully turning them out onto a wire rack to cool.
Meanwhile, prepare the baked eggs. Increase the oven temperature to 170°C (340°F)/fan 150°C (300°F)/gas mark 3½ and generously butter 4 individual ramekins.
Crack one duck egg into each prepared ramekin.
Season the single cream with salt and white pepper, then pour 1 tbsp (15 ml) into each ramekin, being careful to avoid the yolk.
Place the ramekins on a baking tray and bake for 15–20 minutes, until the whites are set but the yolks are still runny, or cooked to your preference.
While the eggs are baking, char the sweetcorn.
Heat a little oil in a frying pan over a high heat.
Add the frozen sweetcorn and a pinch of salt, tossing until it begins to char and pop slightly.
To serve, place a ramekin on each plate alongside a warm tomato and rosemary cake and a handful of fresh baby spinach. Scatter the charred sweetcorn around the plate and finish with a drizzle of white truffle oil over the spinach, if using.