Heat the oven to 355°F (180°C).
Lightly grease a 14x18-inch/37x46 cm rimmed baking sheet and line with parchment paper, smoothing it flat to adhere.
In the bowl of a stand mixer fitted with the whisk attachment, beat the eggs and salt on medium speed until foamy, about 1 minute. Gradually add the sugar and continue beating until the mixture is pale, thick, and tripled in volume, 5 to 7 minutes.
Sift the flour and baking powder directly into the bowl. Gently fold the dry ingredients into the egg mixture with a whisk or spatula until no flour streaks remain. Pour the batter into the prepared pan and spread evenly.
Bake for 10 to 12 minutes, or until the cake is lightly golden and springs back when touched. Cool in the pan on a wire rack for 5 minutes, then remove from the pan and cool completely.
To make the filling, combine the cream, milk, and powdered sugar in a clean mixer bowl. Beat on medium speed until slightly thickened, then add the pudding mix and continue beating until soft peaks form.
Once the cake is cool, invert it onto a clean sheet of parchment paper and gently peel off the baking paper. Spread the jam in a thin, even layer. Spoon on most of the whipped cream and spread it evenly, leaving a small border.
Line the short edge of the cake with sliced strawberries and gently roll the cake into a log, using the parchment to help guide it. Place seam-side down on a serving platter. Spread the remaining cream over the top and decorate with more strawberries. Chill for at least 30 minutes before serving.