Preheat oven to 350 degrees F. Position rack second shelf from the bottom.
Line the jelly roll pan with parchment paper well-fitted in the corners, clipped if possible. Spray with cooking spray to ensure the cake does not stick and for easy removal. Set aside until needed.
Crack eggs into a large mixing bowl. Set timer for 6 minutes and beat eggs on medium-high for no less than 6 minutes. They will look glossy and pale yellow with the consistency of pudding.
Add cake mix, oil, water and vanilla. Blend with a spatula and beat for 1 minute using an electric mixer.
Remove 1-½ cups of batter from the bowl and set aside to make a small jelly roll or cupcakes.
Separate batter evenly into 4-6 bowls, depending on the number of colors wanted.
Add a drop or two of food coloring to each bowl and mix until the colors are uniform throughout as desired.
Transfer batter into 6 resealable bags and cut a small corner off of each bag for squeezing or get ready to spoon batter into pan.
In a diagonal pattern, squeeze strips of each color or spoon until the pan is filled. If you have batter remaining, fill in as needed.
Gently shake the pan to even out the cake batter. Make sure the pan is filled with batter right to the edges.
Using a toothpick, draw swirls in the batter to create a tie dye look.
Bake for 7-9 minutes or until the cake is set. Do not overbake. Remove from oven and allow to cool for 1-2 minutes.
Using a hand-held strainer, gently and evenly tap a ½ cup of icing or powdered-sugar over a tea towel. This will prevent the cake from sticking to the towel. Flip the cake out of the pan and onto the towel. Then dust the top of the cake with the remaining ½ cup of icing or powdered sugar until covered.
Starting at one end, roll the cake up with the towel as tightly as possible. Set it aside to completely cool on a cooling rack for at least one hour, if not two.