Preheat the oven to 350 °F (180 °C); line a 10 × 15-inch (25 × 38 cm) jelly-roll pan with parchment that overhangs by about 2 inches (4 cm) on all sides, then lightly grease and flour the paper.

Whisk the flour, baking powder and salt in a medium bowl.

In a large bowl beat the eggs until pale and voluminous, gradually add the granulated sugar, then pour in the milk and ½ teaspoon vanilla and beat for one more minute.

Add the dry mixture in stages on low speed; once incorporated, increase to medium and beat for another minute.

Spread the batter evenly in the prepared pan, tap the pan to release air bubbles, and bake 10–13 minutes until the center springs back when lightly touched.

Immediately lift the hot cake out with its parchment, roll it up from the short end with the paper still attached, and cool on a wire rack.

For the filling, beat the cream cheese with powdered sugar and the remaining ½ teaspoon vanilla until smooth; whip the cream to stiff peaks and fold it into the cheese in two additions.

Unroll the cooled cake, peel away the parchment, spread the cheesecake filling to the edges, scatter the sliced strawberries over the cream, and re-roll tightly.

Wrap the roll in plastic and refrigerate 4–5 hours or overnight; before serving, liberally dust with powdered sugar, slice, and present immediately.