Heat the oven to 170°C / 340°F. Butter and lightly flour a 22 cm / 9 in round cake pan, or line the base with parchment.
Sift together the cake flour, potato starch, baking powder, and salt. This helps the cake stay airy and lump-free.
In a large bowl, beat the soft butter, sugar, lemon zest, and vanilla until very pale, fluffy, and creamy.
Add the eggs one at a time, beating well after each addition. If the mixture looks slightly curdled, keep going; it will smooth out once the dry ingredients are added.
Fold the sifted dry ingredients into the butter mixture in 2 to 3 additions. Use a spatula and gentle upward motions so the batter stays light.
Transfer the batter to the prepared pan and smooth the top.
Bake for 35 to 40 minutes, until the cake is golden, springy in the center, and a skewer comes out clean.
Let the cake cool in the pan for 10 minutes, then turn it out onto a rack and cool completely.
When fully cool, dust generously with powdered sugar.
Slice and serve on its own, or with softly whipped cream and fresh berries.