Preheat oven to 350°F. Spray a 10x15 inch baking pan with nonstick spray so the parchment paper sticks. Then line it with parchment paper so the cake seamlessly releases when it's done. Spray or grease the parchment paper too.
Sift the flour, cocoa powder, baking powder, and salt together. Set aside.
Using a hand mixer or a stand mixer fitted with whisk attachment, beat the eggs for 5 minutes on high speed. They will be light and very fluffy. On medium speed, beat in the granulated sugar, brown sugar, oil, milk, vinegar, food coloring, and vanilla until combined.
Stop the mixer, pour in the sifted dry ingredients, then beat on low until the batter is completely combined.
Meanwhile, lay a thin kitchen towel or parchment paper flat on the counter. Sprinkle with 1 cup of confectioners' sugar. Once the cake comes out of the oven, immediately invert it onto the towel or parchment paper. Peel off the parchment paper then, starting with the narrow end, begin rolling the cake up with the towel. Do this slowly and gently. The cake will be warm as it just came out of the oven.
Allow the cake to cool completely rolled up in the towel or parchment paper.
Gently and slowly unroll the cake. Flatten it out and spread frosting evenly on top, leaving about a 1/2 inch border around the cake. Gently and slowly roll the cake back up, without the towel or parchment paper this time. Make sure you're rolling it tightly. Some frosting may spill out the sides.
Dust with more confectioners' sugar, if desired.