1) Preheat the oven to 375°F. Line an 18" x 13" half-sheet pan with parchment or aluminum foil, and grease the parchment or foil.
2) Beat the eggs and salt at high speed until they're foamy.
3) Gradually add the sugar, beating till thick and light-colored, about 3 minutes at high speed of an electric or stand mixer.
4) Gently mix in the water and vanilla.
5) Stir in the flour, scraping the bowl to make sure the mixture is thoroughly combined.
6) Pour the batter into the prepared pan, making sure it spreads into the corners.
7) Bake the cake till it's a light golden brown, and a cake tester inserted into the center comes out clean, about 16 minutes.
8) While the cake is baking, generously sprinkle confectioners' sugar on a smooth dish towel (not terry cloth) larger than 18" x 13". Gently rub/spread the sugar to cover the surface of the towel.
9) Remove the cake from the oven, and turn the pan over onto the towel. Lift off the pan.
10) Peel off the parchment or foil. Starting with a short end, gently roll the warm cake and towel into a log.
11) Let the wrapped cake cool for 30 minutes, or until it's completely cool.
12) Unroll the cooled cake, and lift it off the towel onto a clean work surface.
13) Stir the jam till any lumps have smoothed out, and it's soft enough to spread easily. Spread it over the cake.
14) Roll the cake up, again starting with a short end. Roll fairly tight without squashing; you may see excess jam oozing off the edge when you get to the end. That's OK; just scrape it off and use it on your toast.
15) Sprinkle the cake heavily with confectioners' sugar.
16) Let the cake set for an hour or so before serving. For prettiest slices, cut off each ragged end, and serve in 1" slices. A garnish of fruit, sauce, or whipped cream is always welcome.