Preheat the oven to 350 degrees F. Spray a rimmed 10-by-15-inch baking sheet with cooking spray, then line with parchment paper; spray the parchment paper.
In a medium bowl, whisk to combine the cake flour, baking powder and 1/4 teaspoon of the salt. Set aside.
In a stand mixer fitted with the whisk attachment, whisk the egg yolks and granulated sugar until the mixture is light and forms thick ribbons when the whisk is pulled away. Whisk in the 1 teaspoon vanilla extract. With a rubber spatula, fold in the flour mixture until completely combined.
Using a handheld mixer (or stand mixer) fitted with the whisk attachment, beat the egg whites in a large bowl until stiff peaks form, about 3 minutes on medium-high speed. Gently fold the egg whites into the batter until completely combined.
Pour the batter onto the prepared baking sheet and spread with an offset spatula or spoon to evenly cover the parchment. Bake until the cake is springy when touched, about 10 minutes.
Dust a clean kitchen towel with the 2 tablespoons confectioners' sugar, turn the cake out onto the towel, and roll into a log. Let cool.
Whip the cream, 1/4 cup confectioners' sugar, and the remaining 1/4 teaspoon salt and 1/4 teaspoon vanilla into stiff peaks. Set aside for the filling and topping.
To assemble, unroll the cake and spread the strawberry jam to cover the cake. Top with some of the whipped cream mixture, and then roll the cake into a log. Transfer to a serving plate, seam-side down, and top with the remaining whipped cream. Garnish with mint sprigs.