Preheat oven to 375°F (190°C). Line a 10 x 15-inch jelly roll pan (or similar rimmed baking sheet) with parchment paper, letting it hang slightly over the edges. Lightly grease the parchment with butter or nonstick spray to ensure the sponge releases cleanly.

In a large mixing bowl or the bowl of a stand mixer, combine the room-temperature eggs and granulated sugar. Beat on medium-high speed for 5–7 minutes, until the mixture is very pale, thick, and about tripled in volume. It should fall in a thick ribbon from the beaters.

Gently beat 2 teaspoons vanilla extract into the whipped eggs and sugar. In a small bowl, stir together the milk and neutral oil and set aside; you will fold this into the batter later to avoid deflating it.

In a separate bowl, whisk together the sifted cake flour, baking powder, and salt. Sift this mixture over the whipped egg mixture in two additions. Using a large spatula, gently fold the dry ingredients into the eggs, scraping from the bottom and turning the bowl as you go, just until no streaks of flour remain.

Take a small scoop of the batter and stir it into the milk–oil mixture to lighten it. Pour this thinned mixture back into the main batter and gently fold until just combined, keeping as much air in the batter as possible.

Pour the batter into the prepared pan and spread it evenly with an offset spatula, making sure it reaches all corners. Tap the pan gently on the counter to release large air bubbles. Bake for 10–12 minutes, until the top is lightly golden, springs back when touched, and looks set rather than shiny.

While the cake bakes, lay a clean, thin, non-fuzzy kitchen towel on the counter and dust it generously with powdered sugar to create a nonstick surface for the hot cake.

When the cake is done, run a thin knife around the edges of the pan. Carefully invert the hot cake onto the sugared towel and peel off the parchment paper. Starting at one short end, roll the warm cake and towel up together into a log, not too tight but firm enough to hold its shape. Place the rolled cake seam-side down on a rack and let it cool completely, 30–40 minutes.

While the cake cools, in a chilled bowl beat the heavy whipping cream, powdered sugar, and 1/2 teaspoon vanilla extract on medium-high speed until soft to medium peaks form. The cream should be spreadable, not stiff or grainy. Keep refrigerated until ready to use.

Gently unroll the cooled cake. A few small cracks are fine. Spread a thin, even layer of jam over the surface of the sponge, leaving about a 1/2-inch border along the long sides. Dollop the whipped cream over the jam and carefully spread it into an even layer.

Re-roll the cake, this time without the towel, starting from the same short end. Use the towel underneath as support if needed. Wrap the rolled cake tightly in plastic wrap and chill in the refrigerator for at least 30 minutes to set and make slicing easier.

Just before serving, unwrap the roll and place it seam-side down on a serving platter. Dust the top generously with powdered sugar and garnish with fresh berries and/or chocolate shavings or a drizzle of melted chocolate if desired. Slice into 1/2- to 1-inch pieces with a sharp serrated knife, wiping the blade between cuts for clean swirls.