Prepare the pan by lining parchment paper to cover the whole inner sides. If your pan is not leak-proof, wrap the outside with aluminium foil. This cake will be baked with a hot water bath so ensure no water is going in.
Heat milk and oil to approximately 158°F (70°C).
With a hand whisk, quickly mix cake flour into the hot mixture. It will turn lumpy but this is fine.
Add and mix the yolk one at a time. Add salt and vanilla. Mix thoroughly until the dough has a sticky smooth consistency.
At this point, preheat oven to 300°F (150°C). I use top and bottom heat without fan, so adjust your oven accordingly if it uses a different setting. Also, start heating up hot water for the water bath.
Using a hand mixer, beat egg white until foamy with even tiny bubbles. With the mixer running on low speed, gradually sprinkle sugar onto the sides as you mix. After entire sugar is mixed in, switch to high speed and beat until soft peak.
Add 1/3 of beaten egg white (meringue) into the batter. With a wire whisk, mix them thoroughly.
Add another 1/3 of meringue. From here on, we want to gently combine the mixture with a folding motion. Be careful not to deflate the batter. The air inside this fluffy meringue is the key component of a fluffy cake. Mix just until no white streaks are seen.
Add the final meringue. Fold gently just until it is 90% mixed.
Switching to a silicone spatula, check the sides and bottom of bowl for any unmixed batter. Fold just until combined. Do not overmix as the batter loses its air every time we mix.
Pour batter into the pan. Shake the pan to spread it evenly. Tap the pan onto the counter twice to release any big unwanted bubbles.
Place the pan onto a larger deep pan. Pour hot water (around 176°F / 80°C) into the bigger pan up to 1-inch high. Carefully transfer into the oven. I place it on the second bottom rack, so not on the middle rack. Bake for 45 - 55 minutes or until the top is brown, spongy, and dry.
Once baked, remove immediately from its pan and peel-off the paper. This will prevent the cake from shrinking too much. Slice it and let cool on the cooling rack before storing or serve it warm.