Preheat oven to 350°F. Line a jelly roll pan with parchment paper. Spray with nonstick spray.
In a medium bowl, combine together the flour, baking powder, and salt. Set aside.
In a large bowl, add together egg yolks, 1/2 cup of sugar, corn syrup, vanilla, and water. Beat over medium-high speed until pale, about 5 minutes.
In a separate large bowl, add the egg whites and beat on high until soft peaks form. Gradually add the 1/3 cup of sugar in three equal parts. Beat until stiff peaks form.
Add about half of the egg whites to the yolk mixture. Gently fold in using a spatula.
Gradually add the dry ingredients into the batter in three equal parts, gently folding after each addition.
Fold in the oil and then the remaining egg whites. Do not over mix. Be careful not to deflate the mixture.
Pour the batter into the prepared baking sheet. Spread it into an even layer.
Bake for 15-18 minutes until golden and the cake springs back to the touch.
Meanwhile, prepare a kitchen towel by dusting it generously with powdered sugar. Once baked, loosen the edges of the cake with a knife. Flip the cake into the prepared towel. Peel back the parchment paper, then roll the cake up. Allow to cool completely on a wire rack.
Beat the heavy cream with powdered sugar and vanilla until light and fluffy.
Gently unroll the cooled cake. Spread with jam and whipped cream. Roll the cake up. Trim the edges, if desired. Top with powdered sugar.