Butter and flour a 9 inch square pan. Preheat the oven to 350 F. If your eggs aren’t at room temperature, set them in a bowl of warm water.
Set the sugar in a large bowl and zest the lemons over it. Rub the sugar and zest together using your fingers, until it resembles wet sand (this releases the flavorful oils from the zest).
Separately, melt the butter then add it to the sugar along with the salt and vanilla. Whisk this mixture well, for at least a minute.
Add the eggs, one by one, whisking between each addition. Once all the eggs are in, whisk vigorously for a minute - you should have a thick, shiny emulsified batter.
Sift the cake flour into the bowl and add the baking powder, sour cream and lemon juice. Whisk until there are no flour streaks. The batter will be smooth and creamy.
Pour the batter into the prepared cake pan and smooth it into an even layer. Sprinkle the sugar in an even layer on top to coat.
Bake the cake until a cake tester comes out clean, about 30-35 minutes. Allow to cool in the pan. Cake is best eaten the day of. Leftovers can be stored in an airtight container.