Heat oven to 375º degrees F. Lightly coat a jelly-roll pan (a cookie sheet with sides) with vegetable cooking spray. Line the bottom with wax paper. Combine the flour, baking powder, and salt in a small bowl; set aside.
Using an electric mixer at high speed, beat egg whites until foamy. Gradually add 1/2 cup of the granulated sugar, one tablespoon at a time, and continue beating until stiff peaks form.
In another bowl, beat egg yolks and another 1/2 cup of the granulated sugar until pale and thick. Beat in 1 teaspoon of the vanilla. Use a rubber spatula to gently fold the flour and beaten yolks into the whites until just blended. Spread in pan. Bake 15 minutes or until the cake springs back when lightly touched.
Meanwhile, place a clean dish towel on the counter and dust it lightly with confectioners' sugar. When the cake is done, loosen the edges from the pan with a knife and invert the cake onto the towel. Peel off the waxed paper. Roll the cake lengthwise, along with the towel, and set aside, at room temperature, to cool. Can be made up to one day ahead.
Whip the cream with the remaining 1/4 cup of sugar and 1 teaspoon vanilla until soft peaks form. Unroll the cake and spread with half the whipped cream. Top with half the strawberries, and reroll without the towel. Serve with the remaining strawberries and whipped cream.
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