For the cake, heat the oven to 350°F with a rack in the middle position. Trace the bottom of a 9-by-13-inch baking pan on kitchen parchment, then cut inside the line to create a piece to fit inside the pan.

Brush the bottom of the pan with oil, set the parchment over it, then brush the top of the parchment and the sides of the pan with oil. Dust lightly with flour.

In a bowl, whisk together the flour, cocoa, five-spice powder, baking powder, and salt. In a separate bowl, whisk together the egg yolks, 1 cup of the sugar, the water, oil and vanilla.

Add the dry ingredients to the yolk mixture and whisk until well combined. Set aside.

In the bowl of a stand mixer with whisk attachment, whip the egg whites on medium-high until light and foamy, about 1 minute.

With the mixer running, slowly add the remaining ⅓ cup of sugar and continue to whip until the whites are thick and glossy and hold soft peaks, about 3 minutes.

Use a silicone spatula to fold a third of the whipped egg whites into the yolk mixture, then gently fold in the remaining whites until combined.

Transfer to the prepared pan and bake until it bounces back when gently pressed at the center, about 25 minutes, rotating halfway through.

Let cool 1 hour on a wire rack. Once cool, run a knife along the edge of the pan to release cake, then invert onto the rack to remove from the pan. Re-invert onto another rack or cutting board.

For the sauce, in a medium bowl stir together the water and espresso powder together until the espresso is dissolved. Whisk in both milks, the vanilla and salt until smooth. Cover and refrigerate.

For the topping, in a stand mixer with the whisk attachment, whip all ingredients on low until uniform and frothy, about 30 seconds. Increase to medium-high and whip until soft peaks form, about 1 minute.

To serve, cut the cooled cake into 12 squares and transfer to individual serving plates. Spoon about 1 tablespoon of the sauce over each piece, then dollop with topping.

Using a fine mesh strainer, gently dust the top of each serving with cocoa powder. Serve with additional sauce on the side.