Preheat the oven to 350. Line a 10 inch by 15 inch rimmed baking sheet with foil, spray the foil with cooking spray, and lightly dust it with flour.
In a medium bowl whisk together the flour, salt, and baking powder until well combined. Set aside.
In a large bowl or in the bowl of a stand mixer, beat the eggs on high until frothy, about five minutes. Then beat in the sugar, oil, and vanilla. Fold in the flour mixture until just combined.
Divide the cake batter into six bowls. Add red food coloring to the first bowl, yellow and red to the second, yellow to the third, green to the fourth, blue to the fifth, and red and blue to the sixth. Stir each individual bowl of cake batter so that the color is well distributed.
Pour the bowl of red cake batter at the end of the prepared baking sheet. (See photos in the post.) Then repeat with the orange, then yellow, then green, then blue, and finally purple. Tip: Mentally divide the pan into six equal parts and then pour. You don't want to pour the orange batter directly next to the red and so on, because you won't have enough batter to make it to the other end of the baking sheet. But once they are all poured they will spread to cover the whole pan.
Bake for 9 to 11 minutes or until the cake easily springs back when you push on it with your finger.
While the cake is baking spread a clean towel on the counter, sprinkle very liberally with powdered sugar making sure that no area of the towel that will see cake is showing.
As soon as the cake comes out of the oven, flip it over onto the towel and peel away the tin foil carefully. Roll the cake up in the towel. Let the cake cool, rolled up in the towel, for at least an hour, but not longer than four hours.
While the cake is cooling, make the frosting.
