Preheat oven to 350°F (175°C).
Beat 2 egg whites until soft peaks form, gradually adding 1/2 cup sugar and continue beating until stiff peaks develop.
In a separate bowl, sift together 2 1/4 cups cake flour, 3 teaspoons baking powder, 1 teaspoon salt, and 1 1/2 cups sugar.
Add 1/3 cup oil, half of the milk, and 1 1/2 teaspoons vanilla to dry ingredients, beat 1 minute at medium speed.
Pour in the remaining milk and 2 egg yolks, beat 1 more minute, scrape down the bowl.
Gently fold in stiff egg whites.
Divide batter between two greased 9x1.5-inch round pans, bake 25 minutes.
Cool cakes in pans 10 minutes, then turn onto cooling rack until completely cool.
For custard filling, combine 1/3 cup sugar, 1 tablespoon flour, 1 tablespoon cornstarch, and 1/4 teaspoon salt in a saucepan.
Gradually stir in 1 1/2 cups milk, cook while stirring until thick and boiling, continue 2-3 minutes.
Temper egg yolk with a small amount of hot custard, return to saucepan, cook until it boils again.
Remove from heat, add 1 teaspoon vanilla, let cool, beat smooth, fold in 1/2 cup whipped cream.
For chocolate glaze, melt 1 1/2 ounces unsweetened chocolate with 2 tablespoons butter over low heat, stirring constantly.
Remove from heat, stir in confectioners sugar and 1 teaspoon vanilla until crumbly.
Blend in 3 tablespoons boiling water, add additional water as needed to reach pouring consistency.
Assemble cake by spreading custard between cooled layers, pour chocolate glaze over top, spreading evenly over top and sides.