Preheat oven to 375°F (190°C). Line a 10×15-inch jelly roll pan with parchment, leaving overhang. Lightly grease and dust with flour, tapping out excess.
Whisk flour, baking powder, and salt in a bowl. In a separate bowl, beat egg yolks, ½ cup sugar, and vanilla until thick and pale (3–4 minutes).
In another bowl, beat egg whites until soft peaks form. Slowly add ¼ cup sugar and beat to stiff, glossy peaks.
Gently fold egg whites into yolk mixture in three additions. Sift in dry ingredients in three parts, folding gently each time.
Spread batter evenly in the pan and tap gently to remove air bubbles. Bake 10–12 minutes, until golden and springy.
Run a knife around the edges and invert onto a towel dusted with powdered sugar. Peel off parchment. Starting from the short end, roll the warm cake with the towel into a log. Cool completely on a wire rack.
Beat cream cheese, powdered sugar, and vanilla until smooth. Fold in whipped cream until light and fluffy. Stir in half the strawberries.
Unroll the cooled cake and remove the towel. Spread filling evenly, leaving a small border. Add remaining sliced strawberries on top. Gently roll the cake back up without the towel, seam side down.
Wrap in plastic wrap and refrigerate for 2–3 hours. Dust with powdered sugar before slicing. Garnish with extra strawberries if desired.