Preheat oven to 350 degrees. Line a 10 1/2" by 15 1/2" jelly roll pan with baking parchment and lightly coat with nonstick vegetable spray.
Into a large bowl, sift the flour and baking powder together three times.
In a mixing bowl, beat the egg yolks, vanilla, and 1/4 cup of the sugar together until thick, pale yellow and when drizzled, will hold a ribbon shape for 2 seconds on the surface. This should take about 5 minutes.
Fold in the flour mixture.
In another clean, dry mixing bowl, whisk the egg whites with the pinches of salt and cream of tartar until creamy and foamy. With the mixer still running, sprinkle in the remaining 1/4 cup sugar and whisk until the egg whites hold very soft peaks (the consistency of shaving cream).
In thirds, fold the egg whites into the egg yolk mixture. Spread the batter in the prepared pan and bake for 8 minutes, until barely golden. Set the pan on a rack to cool.
Make the vanilla cream filling: With an electric mixer, beat together the vegetable shortening and butter until blended. Turn the mixer down to its lowest setting and gradually add the confectioners' sugar. Turn the mixer back up and beat at high speed until light and fluffy, about 5 minutes. At a drizzle, gradually beat in the vanilla and corn syrup until the filling is the consistency of mayonnaise, about 2 minute more.
Run the tip of a knife around the edge of the cake to loosen it from the sides. Dust the surface with confectioners' sugar. Flip the cake onto a dry work surface. With a spatula, spread a 1/8" thick layer of vanilla cream over the cake. Mix the preserves and water until smooth, then carefully spread 1/3 of it in a very thin layer over the vanilla cream. Roll up tightly. Spread the rest of the preserves around the outside of the roll. Sprinkle the coconut on a cookie sheet. Roll the cake through the coconut to coat completely. Refrigerate for 1 hour to set, then trim the ends even.