Preheat the oven to 375°F / 190°C. Line the bottom of an 8 by 3-inch / 20 by 8cm round cake pan with ungreased parchment and leave the sides of the pan untouched. The cake needs to cling to the ungreased pan to rise properly.
In a large bowl, whisk together the flour and espresso powder and then sift back into the bowl. Set aside.
In a stand mixer fitted with the whisk attachment, whip the egg yolks on high speed. Once the yolks are well combined, turn the speed to medium-low and slowly sprinkle in half the sugar. Turn the speed to high and let it whip for about 5 minutes; it should be light in color and texture and about doubled in volume. When you lift the whisk out of the mixture, the batter should form a ribbon that sits on top of the egg foam for several seconds.
In a clean mixer bowl with a clean whisk attachment, combine the egg whites and salt and beat on low-medium speed until foamy. Slowly sprinkle in the remaining sugar to create a French meringue and, once it is all added, turn the speed to high and beat until stiff, glossy peaks form, 1 to 2 minutes more.
Fold the meringue into the egg yolk foam and then gently stir in the vanilla.
Sift one-third of the flour mixture over the egg foam and gently fold it in. Repeat with the next one-third flour and then the final one-third flour.
Immediately pour the batter into the prepared pan and gently smooth the top with a small offset spatula.
Bake until a tester comes out clean, about 20 minutes. Let the cake cool completely in the pan. Run a knife around the edge before turning out.