Whisk flour, baking powder, salt, and all but 3 tbsp sugar in mixing bowl. Whisk in 2 whole eggs and 3 yolks, butter, water and vanilla; whisk until smooth.
In the bowl of a stand mixer with whisk attachment, beat remaining 3 egg whites at medium low speed until frothy, 1-2 minutes. With machine running, gradually add remaining 3 tbsp sugar, increase speed to medium high and whisk until soft peaks form 1-2 minutes.
Stir ⅓ of whites into batter; add remaining whites and fold until no white streaks remain. Pour batter into prepared pan and bake 30-40 minutes, until a toothpick inserted in the middle comes out clean.
Cool cake in pan 10 minutes, then invert on rack, peel off and discard parchment; invert again and allow to cool completely, approx 2 hours.