In a large bowl, add in the egg yolks, milk, oil, and vanilla extract. Mix until combined.
Sift in the flour and mix until combined. Set aside.
In a separate large bowl, add in the egg whites and cream of tartar. Beat with a hand mixer until frothy.
Gradually add in the sugar 1/3 at a time. Beat until you get stiff peaks
Add some of the egg white mixture to the egg yolk mixture. Gently mix until combined.
Add the egg yolk mixture to the rest of the egg whites. Gently fold until combined.
Separate the batter and dye. Dye ~2/3 of the batter red and the remaining green and white.
Transfer the dyed batter into piping bags. Start with the green batter and pipe a ring along the bottom edge of the cake pan. Then switch to the white batter and pipe a ring right next to the green batter. Fill the center with red batter. Repeat this until you have no more batter.
Drop the cake pan a few times to get rid of any air bubbles
Bake at 285F for 55 minutes
Cool the cake upside down. Remove the cake from the cake pan once cake has cooled.