Preheat your oven to 325°F / 165°C. Generously butter and flour a 9- or 10-inch springform pan and set aside.
In a large bowl, use an electric mixer to beat the egg yolks until they are creamy and light yellow. Gradually add the sugar while continuing to beat.
Continue for about 10 minutes, until the mixture is pale, thick, and fluffy.
With the mixer on low, carefully beat in the boiling water, lemon juice, and vanilla extract for another minute until just combined.
In a separate bowl, sift together the flour and baking powder. Gently fold the sifted dry into the egg yolk mixture in two or three additions, mixing only until no flour streaks remain.
In a clean, dry bowl, beat the egg whites with the salt until they form stiff, glossy peaks. Be careful not to overbeat.
Gently fold about one-third of the egg whites into the batter to lighten it.
Then, carefully fold in the remaining egg whites in two more additions, using as few strokes as possible to maintain the volume.
Gently pour the melted and cooled butter over the surface of the batter. Carefully fold it in, again using minimal strokes, just until incorporated. Avoid the milky solids at the bottom of the butter dish.
Pour the batter into your prepared springform pan and smooth the top lightly with a spatula.
Bake for 40 to 45 minutes. The cake is done when it's golden brown, has started to pull away from the sides of the pan, and a toothpick inserted into the center comes out clean.
Let the cake cool in the pan on a wire rack for 10 minutes before releasing the springform side. Allow it to cool completely on the rack before slicing or decorating.
Don't skip the sift. Sifting the flour and baking powder together removes lumps and aerates the mixture, resulting in a finer, more tender crumb.