Preheat oven to 350 degrees F
Place egg yolks in a mixing bowl. Add 1/4 cup sugar and whisk until sugar is dissolved and yolks are lightened in color. Drizzle in vegetable oil, whisking constantly until incorporated. Whisk in milk, vanilla extract, and salt. Add some pink and a tiny bit of red food coloring.
Sprinkle sifted cake flour over the batter and fold until incorporated.
In a clean mixing bowl or the bowl of a stand mixer fitted with the whisk attachment, beat egg whites until frothy. Add the remaining 2 tablespoons of sugar and beat on high speed until whites hold medium-stiff peaks.
Fold a third of egg whites into batter to lighten it, then add the remaining egg whites and fold until just incorporated.
Pour batter over top of the frozen design, spreading the batter into an even layer using a large offset spatula. Bang the pan a few times on the countertop to remove any air bubbles and level out the top.
Bake for about 10 minutes or until the top is springy and the edges are just barely starting to brown.
Remove from oven. Carefully invert warm cake onto a piece of parchment backed by a solid surface like a large cutting board. Peel off parchment paper backing, revealing the design.
Liberally dust a clean towel with powdered sugar and lay it on top of the cake. Flip cake over so the design is facing down.
Starting with the side of the cake without the design, carefully roll up the warm cake in the towel. Doing this while the cake is still warm will mold the cake into a rolled shape and makes it easier to roll it back up later with the filling.
Let rolled cake cool for about 1 hour or until completely cool to the touch.