Line a 12" x 17" sheet pan with a silicone mat or parchment paper.*
Sift powdered sugar into a small bowl. Sift flour into another.
Cream butter and powdered sugar with a wooden spoon till smooth and pale. Add egg white and sifted flour and cream until smooth.
Separate paste and add a small amount of color gel into each using a toothpick.
Spread onto silicone mat in a swirling pattern, alternating colors. Place in fridge to set as you make the cake batter.
Preheat oven to 450F.
Whisk flour and cornstarch in a small bowl. Set aside.
Separate 2 eggs. Place whites into a grease free bowl and set aside.
Place the two yolks into the bowl of an electric mixer fitted with the paddle attachment. Add additional 2 eggs, reserved egg yolk and 1/2 cup of sugar. Beat on high for 5 minutes, until pale and tripled in volume. Beat in vanilla. **
Sift flour mixture over beaten eggs in 2 batches. Fold in until no streaks of flour remain.
Clean mixer bowl (if you don't have an extra) and wipe down with lemon juice to ensure there is no trace of grease.
Whip egg whites until foamy and add in cream of tartar. Whip until soft peaks and slowly add in 1 Tbsp of sugar. Whip until stiff peaks.
Gently fold whites into cake batter. Spread evenly in pan (on top of chilled color paste) and bake for 7mins or until cake is golden brown and springs back to the touch.
While still hot, loosen the edges with a small metal spatula or knife. Sprinkle cake lightly with powdered sugar and turn out onto parchment.
If using a silicone mat:
Flip cake over again with the silicone mat attached and roll up with the mat. Roll entire thing in a clean dish towel and allow to cool.
If using parchment:
Remove parchment from bottom of cake. Sprinkle powdered sugar over a clean tea towel. Flip cake over onto tea towel, roll up, and allow to cool completely.
Place mixer bowl and whisk into the fridge for 30mins to chill.
Place cream, sugar, and vanilla into mixer bowl and whip on high until stiff peaks.
Gently unroll cake. Spread whipped cream evenly over surface leaving a 1/2" border. Roll up tightly and refrigerate for 30mins or up to 3 hours. Serve same day.
* If using parchment paper - spray sheet pan with cooking spray, line with parchment and spray again. ** At this point i transferred the beaten eggs to a large bowl as I needed to reuse the mixer bowl for the whites. Watch this video for more information on how to make and roll the cake. Cake roll recipe adapted from Rose Levy Beranbaum's The Cake Bible.