In a large bowl, by hand, whisk 1 1/4 cup flour, 1 1/2 tsp baking powder, 1/4 tsp salt, and all but 3 T of the 1 cup sugar in mixing bowl. Add 2 whole eggs and 3 yolks (reserve whites), 6 T melted/cooled butter, 2 T water, and 2 tsp vanilla, and whisk until smooth. Set batter aside.
Using a mixer fitted with whisk attachment, beat 3 egg whites at medium-low speed until frothy, 1-2 minutes. With machine running, gradually add the remaining 3 T sugar, increase speed to medium-high, and beat until soft peaks form, 60-90 seconds.
Stir 1/3 of egg whites into batter to lighten. Add the remaining egg whites and gently fold into batter until no white streaks remain.
Pour batter into prepared pan and bake 30-40 minutes (until top springs back when touched).
Cool in pan 10 minutes, then invert cake onto greased wire rack; peel off and discard parchment. Cool completely, about 2 hours.