Preheat the oven to 350 °F (175 °C). Line a 10 × 15‑inch jelly‑roll pan with parchment paper, leaving an overhang for easy removal.

Make the sponge: In a large bowl, beat the egg yolks with sugar until pale and thick. Stir in vanilla, milk, and melted butter. In a separate bowl, whisk the egg whites with a pinch of salt until soft peaks form, then gently fold them into the yolk mixture. Sift in the flour, baking powder, and salt; fold gently to combine. Spread the batter evenly into the prepared pan and bake for 10–12 minutes, until the cake springs back when touched.

Immediately turn the warm cake out onto a clean kitchen towel lightly dusted with powdered sugar. Peel off the parchment paper and, using the towel, roll the cake from the short end. Let it cool completely while rolled to set its shape.

Make the raspberry sauce: In a small saucepan, combine the raspberries, sugar, and lemon juice. Simmer for about 5 minutes until the berries break down. If using, stir in the cornstarch mixed with a little cold water and cook until slightly thickened. Strain the sauce through a fine‑mesh sieve to remove seeds. Let cool.

Make the filling: Melt the white chocolate with the heavy cream until smooth, then let it cool slightly. In a mixing bowl, beat the mascarpone (or cream cheese) with the powdered sugar and vanilla until creamy, then fold in the melted white chocolate mixture until smooth and fluffy.

Assemble the log: Carefully unroll the cooled cake. Spread the white chocolate filling evenly over the surface. Drizzle or spread the raspberry sauce over the filling. Then roll the cake back up (without the towel) and place seam‑side down on a serving platter.

Decoration: Spread whipped cream or white chocolate ganache over the roll. Decorate with fresh raspberries, white chocolate curls or shavings, and dust with powdered sugar for a “snow‑dusted” effect.