Preheat oven to 350°F. Line a jelly roll (10x15”) pan with foil and spray with cooking spray (I like to use the spray with flour).
Beat eggs at high speed for 3 minutes, until frothy and dark yellow. Beat in sugar, coffee, and vanilla extract.
Whisk together cocoa, salt, baking powder, and flour. Stir into wet ingredients just until blended.
Spread in prepared pan. Batter will be in a very thin layer and you will need to use a wooden spoon or spatula to spread it to all the corners of the pan. Bake for 9-11 minutes (mine took 10).
While the cake is baking, set a clean kitchen towel out on a large work surface. Sprinkle liberally with powdered sugar (about 1/4 cup). As soon as the cake comes out of the oven, turn it over on the kitchen towel sprinkled with powdered sugar. Remove foil carefully.
Working at the short end, fold the edge of the towel over the cake. Roll tightly, rolling up the cake into the towel. Let cool completely while rolled, at least one hour (or overnight).