Preheat oven to 375°F and line a 10x15-inch jelly roll pan with parchment paper.
Beat eggs on high speed for 3 minutes until pale and thick.
Add sugar gradually and fold in vanilla.
Sift dry ingredients and gently fold into egg mixture.
Add milk, pour batter into pan, and bake for 10–12 minutes.
Flip hot cake onto a towel dusted with powdered sugar and roll it tightly.
Cool the rolled cake for 30 minutes.
Whip cold cream with powdered sugar and vanilla until stiff peaks form.
Fold in raspberries and raspberry jam gently.
Unroll cooled cake, spread filling evenly, then re-roll tightly.
Dust with powdered sugar and chill for at least 1 hour before serving.