Preheat the oven to 160°C (320°F). Prepare a tube pan or cake pan; do not grease if using a tube pan (the cake benefits from sticking to the sides while rising).
In a mixing bowl, whisk together the 4 egg yolks and 2 tablespoons of the sugar until the mixture is pale and slightly increased in volume.
Whisk the corn oil and milk into the egg yolk mixture until combined.
Sift (or add) the self-raising flour and Parmesan cheese into the yolk mixture and stir gently until a smooth batter forms; set aside.
In a clean bowl, beat the 4 egg whites on high speed until foamy. Gradually add the remaining sugar (from the 1/2 cup) while beating and continue until soft peaks form.
Sprinkle in the tablespoon of corn flour (cornstarch) and beat briefly to combine without deflating the whites.
Fold one-third of the beaten egg whites into the yolk batter using a hand whisk to loosen it, then gently fold in the remaining egg whites with a spatula until just combined and no large streaks remain.
Pour the batter into the prepared pan and smooth the top. Bake at 160°C (320°F) for about 40 minutes, or until a skewer inserted near the center comes out clean.
Immediately invert the pan and let the cake cool completely while upside down to preserve its height, then remove from the pan and serve with whipped cream or buttercream and extra shredded Parmesan and cheddar if desired.