1. Preheat oven to 350 degrees. Line a 9-by-13-inch baking pan with parchment paper, and set aside. Sift together flour, salt, and baking powder in a medium bowl.

2. In the bowl of an electric mixer fitted with the whisk attachment, beat together egg yolks and sugar on medium-low speed until light and fluffy. Beat in the water and vanilla bean scrapings. Add dry ingredients in three batches, scraping down sides of bowl with a rubber spatula as needed, just until flour mixture is incorporated after each addition.

3. In another mixing bowl, beat egg whites until stiff but not dry peaks form; whisk a quarter into batter to lighten. Fold in remaining egg whites, and pour batter into prepared pan. Bake until cake springs back when gently pressed in the center, 15 to 20 minutes. Transfer to a wire rack to cool completely.