Preheat oven to 375 degrees F. Grease a jelly roll pan; line with parchment or waxed paper and grease paper.
Stir together the flour, sugar, baking powder, and salt in a large bowl. Add the butter, 2 eggs, and the vanilla to the dry ingredients and beat with an electric mixer on high speed until fluffy. Separate the remaining 2 eggs. Place the whites in a small bowl and beat the yolks into the batter.
With clean beaters, beat the egg whites at high speed until they are stiff; fold beaten whites into the batter just until no white streaks remain.
Spread batter into the prepared pan and bake until the center springs back when lightly pressed, about 15 minutes.
Sift confectioners' sugar over a linen towel that has been spread out on a work surface; invert cake onto towel. Quickly, remove parchment, trim off crisp cake edges, spread cake with jam, and roll up using towel as an aid. Tightly roll cake in towel and set aside, open side down, until completely cool, about 30 minutes. Transfer to serving plate and slice crosswise.
Recipe courtesy Joanne Lamb Hayes, Grandma's Wartime Baking Book, St. Martin's Press, 2003