Practically any variation on the batters below will work here; if using a smaller 15 ½ × 10 ½-inch jelly-roll pan, halve the batter recipes.
Preheat the oven to 325°F. Grease a 17 ½ × 11 ½ × 1-inch rimmed baking sheet and line the bottom with parchment paper.
Prepare the batter for one of the following:
Scrape the batter into the pan, spreading evenly, until it is two-thirds full (there may be a cup or two of batter leftover). Bake until the top springs back when lightly pressed, 15 to 20 minutes.
While the cake is still warm, run a knife along the edges to release it from the pan. Immediately invert the cake onto a sheet of parchment paper and remove the pan. Let the cake cool completely before peeling off the paper liner.
Peel off the paper liner and place a fresh sheet of parchment paper on top. Flip the cake and peel off the parchment paper the cake was cooled on, removing the brown “skin” from the cake as you do so.
If using French Sponge Cake, Génoise, or Chocolate Génoise, brush the cake with:
Spread it with:
using the smaller amount for richer fillings or frostings and the larger amount for fluffier, lighter fillings or frostings. Starting on a short side, fold and press an inch or so of the cake firmly up over the filling to get started. Keep these first turns tight; cracking will diminish as the diameter of the roll increases. Use the parchment under the cake to help roll the cake. Once the cake is rolled, use two hands to move the roll carefully back to the center of the parchment. Wrap the back of the parchment over the cake so that it overlaps the front portion of parchment, covering the roll completely. Place the edge of a cookie sheet right next to the long side of the cake roll, where it meets the parchment, and tighten the cake roll by pressing the baking sheet at an angle toward the counter while you grasp the bottom sheet of parchment, shown below. Then wrap the tightened cake roll in the parchment and fold the ends. Refrigerate at least 1 hour to firm the roll before unwrapping and serving.
If desired, sift over the cake before serving: