Preheat the oven to 375 degrees F (190 degrees C). Line a 10x15 inch jellyroll pan with parchment paper.
Sift together the flour, baking powder and salt. Set aside. In a large bowl, beat eggs and sugar with an electric mixer until thick and pale, about 5 minutes. Stir in the vanilla and milk. Stir in the dry ingredients gradually. The batter will be thin. Pour into the prepared pan.
Bake for 8 to 10 minutes in the preheated oven, until the center springs back when pressed lightly. Don't over bake, or it may crack.
Generously dust a clean dish towel with confectioners' sugar. Turn the cake out onto the towel, and peel off the parchment paper. Gently roll up the cake using the towel, and let cool for about 10 minutes.
Unroll the cake, and spread an even coating of jam onto the top. Roll the cake back up into a tight spiral, and remove the towel. Dust with confectioners' sugar before serving.