Preheat your oven to 180°C (350°F). Grease a 9-inch round cake pan with a little olive oil and line the bottom with parchment paper to ensure easy removal.
In a medium bowl, whisk together the all-purpose flour, baking powder, and a pinch of salt until evenly combined. Set this dry mixture aside.
In a large mixing bowl, crack in the eggs and whisk until slightly frothy, about 30 seconds. Add the superfine sugar and continue whisking until the mixture turns pale and slightly thickened, roughly 1 minute.
Pour in the olive oil and add the lemon zest, then whisk until the mixture looks glossy and fragrant, about another minute. The aroma should be fresh and citrusy with a hint of grassy notes from the oil.
Gradually fold the dry ingredients into the wet mixture using a spatula, mixing gently until just combined. Be careful not to overmix; a few lumps are fine to keep the batter light and airy.
Pour the batter into your prepared pan and smooth the surface with the back of a spatula. Gently tap the pan on the counter to settle the batter and release any air bubbles for an even bake.
Bake in the preheated oven for 35 to 40 minutes, or until the top turns a deep golden brown and a toothpick inserted into the center comes out clean. The cake should smell fragrant and slightly fruity.
Remove the cake from the oven and let it cool in the pan for about 15 minutes. Then, transfer it to a wire rack to cool completely, which helps set the crumb and makes it easier to serve.
Once cooled, dust the cake with powdered sugar or drizzle with honey for added sweetness and aroma. Slice and serve at room temperature to best enjoy the rich, fruity olive oil flavor.