Separate 3 eggs into yolks and whites. Place the egg yolks in a large bowl, and set aside on the countertop. Keep the egg whites in another large mixing bowl in the fridge.
In a separate large mixing bowl, mix cake flour and vegetable oil until smooth. Add milk and vanilla extract and mix until well combined.
Pour the egg yolks into the cake flour vegetable oil mixture. Mix until smooth. Set aside.
Grease a 9” x 3” round cake pan with a removable bottom and line the bottom with round parchment paper. Preheat oven to 300°F (150°C).
Remove the egg whites mixing bowl from the fridge, and add cream of tartar and one-third of the sugar into the egg whites. Use a hand mixer or a stand mixer to whip the egg whites for 2 minutes.
Add half of the remaining sugar into the egg whites, and use medium-low speed to whip the egg whites for 2 more minutes until they look smooth.
Add the remaining sugar into the egg whites and keep whipping with medium-low speed until medium peak forms.
Scoop ⅓ of the egg whites into the egg yolk mixture and fold until well combined.
Transfer the egg yolk mixture to the egg white bowl, and gently fold until the color looks even. Do not overmix.
Pour the batter into the prepared cake pan, and gently spread the batter with a spatula. Lightly tap the pan against the countertop to release any air bubbles out of the batter. This will also allow the batter to fill all those nooks and crannies in the pan as well.
Bake at 300°F (150°C) for 15 minutes covered with foil then uncover and bake for 20 more minutes or until a toothpick comes out clean when it’s inserted near the center of the cake.
Remove the cake pan from the oven, immediately flip it upside down, and allow it to cool completely on a wire rack.
Once cooled, insert a small knife between the cake and the sides of the cake pan, and run it around. Place a wire rack on top of the cake pan and flip the entire thing upside-down. The cake should fall on top of the wire rack. Take the removable bottom and the parchment paper off.
Put together the cake pan and put the chiffon cake back in. Brush with simple syrup. Place plastic wrap on top of the cake pan and set it aside until needed.