Preheat oven to 350ºF/175ºC.
Separate the egg yolks and whites into two bowls. Keep the egg whites in the refrigerator, and the egg yolk at room temperature.
Using a fine-mesh sieve, sift the cake flour, baking powder, and matcha powder over a large mixing bowl. Set it aside.
In a separate large bowl, mix the egg yolks and half of the sugar (¼ cup, 50 g) and whisk until the egg mixture becomes lightened in color and double in volume. Set it aside.
In another bowl, beat the cold egg whites with an electric hand mixer or stand mixer until foamy.
Gradually add the remaining sugar (¼ cup, 50 g) over three separate times and beat until stiff peaks form and egg whites are glossy.
Gently whisk in ⅓ of the egg whites to the egg yolk mixture until incorporated in the batter. Then add the mixture back into the egg whites. Gently fold in egg whites with a silicone spatula.
Add the dry ingredients to the egg mixture. Fold in gently until just incorporated by using the silicone spatula. Do not overmix the batter. Overmixing will cause the cake to turn out flat.
Add the warm milk and fold in until incorporated.
Take out the jelly roll pan with decorations from the freezer and pour the matcha batter over top of the frozen design, spreading the batter into an even layer using a large offset spatula. Tap the jelly roll pan a few times on your working surface to remove the air bubble inside the batter.
Bake for 10-12 minutes, or until an inserted toothpick comes out clean and the top of the cake springs back when touched. Be careful not to overbake to avoid cracking.
Remove from oven. Quickly and 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.
Place a new parchment paper on top of the warm 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 parchment paper. 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 the rolled cake cool for about 1 hour or until completely cool to the touch.