Heat the oven to 375 degrees.
Generously butter a 15x10 jelly roll pan. Cut a piece of parchment or waxed paper to fit the inside of the pan. Place the paper in the pan and butter it as well.
Beat the eggs until very thick and pale yellow colored. This will take about 5 minutes. Gradually beat in the sugar. With the mixer on low speed, slowly add the water and vanilla. Still on low speed, gradually add the flour, baking powder, and salt, beating just until blended.
Pour the batter into the prepared pan. Be sure to spread the batter into the corners.
While the cake is baking, prepare a tea towel with a generous dusting of powdered sugar.
Bake for 12-15 minutes or until a toothpick inserted in the center comes out clean. Remove the cake from the oven, loosen it from the edges of the pan, and immediately invert the hot cake onto the prepared tea towel. Carefully peel away the paper. While still hot, carefully roll the cake and towel starting from the narrow end. Cool the rolled cake on a wire rack for at least 30 minutes.
Unroll the cake and remove the towel. Trim away any stiff edges if necessary. Spread the jam or jelly over the inside surface of the cake. Re-roll the cake.
Wrap the cake loosely in waxed or parchment paper and refrigerate. When ready to serve, sprinkle generously with powdered sugar.