Preheat the oven to 350°F. Line a baking sheet with parchment and grease with butter.
In a stand mixer fitted with the whisk attachment, whip the egg yolks on high speed. Once the eggs are well combined, turn the speed to medium-low and slowly sprinkle in half the sugar. Turn the speed to high, and slowly drizzle in the hot espresso. Let it whip for about 5 minutes until the egg mixture is light in color and very thick.
In a clean mixer bowl with a clean whisk attachment, whip the egg whites on medium speed until they start to foam. Slowly sprinkle in the remaining sugar to create a French meringue, turn the speed to high and beat until stiff, glossy peaks form, about 1 to 2 minutes more.
Mix about a third of the meringue into the yolks to lighten the yolk mixture. Gently fold the remaining meringue mixture into the yolks using a rubber spatula.
Combine the flour and salt and sift one-third of the mixture over the egg foam and gently fold it in with a rubber spatula. Repeat with the next one-third flour and then the final one-third flour.
Spread the cake batter over the prepared baking sheet and smooth the top with a small offset spatula.
Bake for about 15 minutes, or until the cake springs back when gently pressed. Allow the cake to cool completely.