Prepare a 16x16cm square pan and line it with parchment paper. Make sure the paper extends 5cm above the rim of the pan.

Separate 5 eggs into whites and yolks.

Cover the bowl of egg whites with plastic wrap and place it in the refrigerator until needed.

In a pot, combine milk, cooking oil, and unsalted butter. Heat over low heat until the butter is 90% melted.

Remove from heat and whisk to melt the remaining butter with residual heat.

Add salt and vanilla extract, then mix.

Sift in the cake flour and whisk until smooth.

Add the 5 egg yolks and whisk until the batter is smooth and lump-free.

Using a hand mixer, whip the chilled egg whites until large bubbles form.

Add 80g of sugar in three parts, whipping between each addition. First, whip until the foam is like cappuccino.

Continue whipping, adding sugar, until the meringue has a subtle sheen.

Add the final part of sugar and whip on medium speed until soft peaks form (the tips should bend).

Fold about a third of the meringue into the yolk batter to lighten it.

Pour the lightened yolk mixture back into the remaining meringue.

Gently fold the batter until just combined, scooping from the bottom up to avoid deflating the meringue.

Pour the batter into the prepared pan from a height of about 20cm.

Use a skewer to pop large air bubbles and level the surface. Tap the pan on the counter to release more air.

Place the cake pan in a larger pan and pour hot water into the outer pan for a water bath.

Place on the lowest rack of a preheated oven and bake at 150°C (300°F) for 55-60 minutes.

After baking, remove the cake from the oven.

Let it cool slightly, then carefully remove the parchment paper.

Once cooled, slice the castella cake and serve.