Preheat oven to 350 degrees. Spray 12x17 rimmed baking sheet with nonstick spray. Add a sheet of parchment paper and spray that with nonstick spray too. We need to make sure the cake doesn't stick to the pan.
Separate eggs and place egg whites in a large bowl for a stand mixer. Whip egg whites and sugar together until stiff peaks form. Place into another bowl and set aside. Add flour, cocoa powder, baking powder and salt to the same bowl. Whisk together. Set aside.
In a separate bowl, add egg yolks and brown sugar together and whisk until smooth and light, about 2 minutes. Add melted butter, vanilla extract, and coffee and whisk to combine. Pour egg mixture over flour mixture. Mix together just until combined.
Add 1/3 of whipped egg whites to mixture and gently fold together. Add next 1/3 of mixture and fold together. Finally, add the last 1/3 mixture and fold together. Pour mixture into prepared baking sheet. Spread into one even layer. Bake in preheated oven until cake bounces back when you touch it, about 10-12 minutes.
While the cake bakes, lay a thin kitchen towel on the counter. Sprinkle with a thin layer of cocoa powder on it. When the cake is finished baking, flip cake over onto the powdered towel. Gently roll the cake up into the towel. Place it into the refrigerator to chill until completely cool, about 1 hour.