Preheat the oven to 350F.
Butter the inside of a half sheet pan (18″ x 13″ x 1″ high), and flour the sides, tapping out the excess flour. Line it with a piece of parchment paper on the bottom, and spray cooking spray on the parchment. Set aside.
Lay a clean tea towel out on the counter and evenly sprinkle the top with powdered sugar.
Whisk together the flour, cornstarch, ginger, cinnamon, allspice, nutmeg, cloves, black pepper, baking soda, and salt in a medium bowl.
Beat the eggs in a large bowl until tripled in volume. Add the brown sugar and beat until thick, about 2 minutes.
Add the dry ingredients to the egg/sugar mixture and stir just until combined, being careful not to over-mix.
Pour the batter out onto the prepared pan and spread it out evenly.
Bake until the cake springs back when you touch it, about 10 to 12 minutes.
Turn the cake out onto the prepared tea towel and peel off the parchment paper. Starting at one of the short ends, roll the cake up in the tea towel into a log shape.
Transfer the cake to a wire rack to cool completely, about 2 hours.