Prep the pan and oven: Heat the oven to 375°F (190°C). Line a 10x15-inch jelly roll pan with parchment, leaving a little overhang.
Lightly grease the parchment to ensure an easy release.
Set up a sugared towel: Lay a clean kitchen towel on the counter and dust it generously with powdered sugar. This prevents sticking when you roll the warm cake and adds a delicate finish to the outside.
Whip the eggs and sugar: In a large bowl, beat the eggs and granulated sugar with a hand mixer or stand mixer on high for 5–7 minutes, until thick, pale, and tripled in volume. The mixture should leave ribbons when you lift the beaters.
Flavor and loosen: Mix in the vanilla and lemon zest.
Drizzle in the milk and gently beat just to combine. Don’t overmix—keep the batter airy.
Combine dry ingredients: In a separate bowl, whisk the flour, baking powder, and salt. Sift or lightly sprinkle the dry mixture over the whipped eggs in three additions, folding gently with a spatula after each.
Use slow, sweeping motions to avoid deflating.
Spread and bake: Pour the batter onto the lined pan and smooth to the edges. Aim for an even layer. Bake 10–12 minutes, until the top springs back when touched and is lightly golden.
Do not overbake.
Turn out and roll warm: Run a knife around the edges to loosen. In one quick motion, invert the hot cake onto the sugared towel and peel off the parchment. While still warm, use the towel to roll the cake from a short side into a tight log.
Let it cool rolled, seam-side down, 20–30 minutes.
Prepare the filling: Stir the jam with lemon juice if using. If the jam is very thick, warm it slightly so it spreads easily without tearing the sponge.
Unroll and fill: Gently unroll the cooled cake. Spread a thin, even layer of jam, leaving a 1/2-inch border on all sides.
Too much filling can cause slipping or oozing.
Reroll and set: Tightly reroll the cake without the towel, keeping it snug but not squished. Wrap in plastic and chill 20–30 minutes to set the swirl and make slicing cleaner.
Finish and serve: Unwrap, dust generously with powdered sugar, and trim both ends for neat slices. Cut with a sharp, serrated knife using gentle sawing motions.