Preheat the oven to 355 degrees F/180 degrees F. Butter and flour an 8-inch/20 cm cake pan and line the bottom with a parchment paper round. Beat eggs (at room temperature) with a fork lightly and set aside. Using a flour sifter, sift flour, salt, and baking powder (if used) two times in a medium bowl.

To make the cake batter, place the softened butter, sugar, lemon zest, and scraped seeds of the vanilla pod in a large bowl or the bowl of a stand mixer. Using an electric or stand mixer fitted with a whisk attachment, whip it for about 15 minutes until the mixture obtains a white and velvety consistency.

Reduce the speed to low and continue whisking. Add the eggs mixture one tablespoon at a time when the last spoonful has been incorporated perfectly. Continue in the same way until the eggs are used up. Remove the mixer's bowl from the mixer and start adding the sifted flour mixture a little at a time (1 tablespoon), incorporating it with large movements using a rubber spatula. Wait for the flour to be absorbed entirely; then add the next spoon. Continue until the dry ingredients are mixed into a creamy mixture.

Pour the batter into the prepared cake pan and smooth it with a rubber spatula. Bake it in the preheated oven for 30 to 40 minutes. Check the cake's doneness with a toothpick: it must come out dry.

Remove the cake from the oven and, while it is hot, invert it on a flat serving platter lined with parchment. Let it rest for about 15 minutes, no longer to prevent the formation of condensation on the paper.  Then using a plate or a cutting board, turn it over again. This little trick helps obtain a perfectly flat top. Let the cake cool down completely on a wire rack (it takes up to an hour). Sprinkle generously with powdered sugar.