Preheat oven to 400°F (200°C) and line a 9x13 inch baking sheet with parchment paper, leaving an inch overhang.

Separate 3 eggs into yolks and whites, ensuring no yolk is in the whites, then let sit at room temperature for 10 minutes.

In a large bowl, beat the egg yolks with 3/4 cup caster sugar for 3 minutes until pale and ribbon-like.

In a clean medium bowl, whip the egg whites with a pinch of salt until stiff, glossy peaks form.

Add 1 teaspoon vanilla extract and 2 tablespoons warm water to the yolk mixture, sift in the flour and baking powder, and fold gently to combine.

Fold the whipped egg whites into the batter in two batches, keeping the mixture light and airy.

Spread the batter evenly on the prepared sheet and bake for 12 minutes until golden and springy to the touch.

Turn the warm cake out onto a clean kitchen towel, peel off the parchment paper, and let cool for 5 minutes.

Whip 1/2 cup heavy cream with 2 tablespoons powdered sugar and 1/2 teaspoon vanilla extract until soft peaks form.

Spread the jam evenly over the warm cake, leaving a 1/4 inch border, then spread the whipped cream on top and roll tightly using the towel.

Chill the roll seam-side down for at least 30 minutes, then dust generously with powdered sugar before slicing and serving.